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| CMS-HIG-21-018 ; CERN-EP-2026-009 | ||
| Combined measurements and interpretations of Higgs boson production and decay in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 20 February 2026 | ||
| Submitted to Reports on Progress in Physics | ||
| Abstract: Combined measurements of Higgs boson production and decay rates are reported, representing the most comprehensive study performed by the CMS Collaboration to date. The included analyses use proton-proton collision data recorded by the CMS experiment at $ \sqrt{s}=13 \text{TeV} $ from 2016 to 2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. The statistical combination is based on analyses that measure the following decay channels: $ \mathrm{H}\to\gamma\gamma $, $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $, $ \mathrm{H}\to\mathrm{W}\mathrm{W} $, $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\mathrm{b}\mathrm{b} $, $ \mathrm{H}\to\mu\mu $, and $ \mathrm{H}\to\mathrm{Z}\gamma\to\ell\ell\gamma $ ($ \ell=\mathrm{e},\mu $). Information in the events from each decay channel is used to target multiple Higgs boson production processes. Searches for invisible Higgs boson decays are also considered, as well as an analysis that measures off-shell Higgs boson production in the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ decay channel. The best fit inclusive signal yield is measured to be 1.014 $ ^{+0.055}_{-0.053} $ times the standard model expectation, for a Higgs boson mass of 125.38 GeV. Measurements in kinematic regions defined by the simplified template cross section framework are also provided, as well as interpretations in the coupling modifier and standard model effective field theory frameworks. The coupling modifier interpretation is further used to place constraints on various two-Higgs-doublet models. The results show good compatibility with the standard model predictions for the majority of the measured parameters. | ||
| Links: e-print arXiv:2602.18611 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Examples of leading-order Feynman diagrams for the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ and $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ decay channels (upper left); for the $ \mathrm{H}\to\mathrm{b}\mathrm{b} $, $ \mathrm{H}\to\tau\tau $, and $ \mathrm{H}\to\mu\mu $ decay channels (upper right); and for the $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{Z}\gamma $ decay channels (lower). |
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Figure 2:
Examples of leading-order Feynman diagrams for the $ \mathrm{ggH} $ (upper left), $ \mathrm{VBF} $ (upper middle), quark-initiated $ \mathrm{VH} $ (upper right), gluon-initiated $ \mathrm{ZH} $ (middle left), $ \mathrm{ttH} $ and $ \mathrm{bbH} $ (middle right), $ \mathrm{t}\mathrm{H}\mathrm{q} $ (lower left), and $ \mathrm{t}\mathrm{H}\mathrm{W} $ (lower right) processes. |
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Figure 3:
Breakdown of the 68% CL intervals on the best fit inclusive and per production process (left), and per decay channel (right) signal strength modifiers, for the different sources of uncertainty. The uncertainty contributions are shown as percentages relative to the best fit signal strength values. All contributions are symmetrized by taking the average of the upward and downward fluctuations. The ``Misc.'' label absorbs all other uncertainty contributions not listed explicitly in the figure. The NPs from each uncertainty source are sequentially fixed to their best fit values to derive the individual contributions following the order in which they are shown in the figure. The total uncertainty is shown by the dashed red boxes, while the combined systematic uncertainties from experimental and theoretical components are shown in orange and purple, respectively. The uncertainties for the $ \mu^{\mathrm{tH}} $, $ \mu^{\mu\mu} $, and $ \mu^{\mathrm{Z}\gamma} $ parameters are multiplied by a factor of 0.5. |
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Figure 4:
The measured inclusive ($ \mu^{\text{incl}} $) and per production process ($ \mu^i $) signal strength modifiers. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{tH}} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 6 parameters in the per production process measurement are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 4-a:
The measured inclusive ($ \mu^{\text{incl}} $) and per production process ($ \mu^i $) signal strength modifiers. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{tH}} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 6 parameters in the per production process measurement are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 4-b:
The measured inclusive ($ \mu^{\text{incl}} $) and per production process ($ \mu^i $) signal strength modifiers. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{tH}} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 6 parameters in the per production process measurement are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 5:
The measured per decay channel signal strength modifiers, $ \mu^f $. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{Z}\gamma} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 7 parameters considered in this fit are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 5-a:
The measured per decay channel signal strength modifiers, $ \mu^f $. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{Z}\gamma} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 7 parameters considered in this fit are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 5-b:
The measured per decay channel signal strength modifiers, $ \mu^f $. In the upper plot, the thick (thin) black lines indicate the 68% (95%) CL intervals, with the theoretical systematic, experimental systematic, and statistical components of the 68% intervals indicated by the purple, orange, and blue bands, respectively. The grey band shows the 68% CL interval on the inclusive signal strength modifier. A separate axis is provided for the $ \mu^{\mathrm{Z}\gamma} $ parameter because of its larger uncertainty and high best fit value. The correlations between the 7 parameters considered in this fit are shown in the lower plot. The size of the correlations is indicated by the colour scale. |
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Figure 6:
Summary of the signal strength modifier measurements. The empty circles and black lines represent the best fit points and 68% CL intervals, respectively. The orange lines indicate the systematic components of the total 68% CL intervals. The left-hand panel shows the measurements of the per decay channel signal strengths, while the grey band shows the 68% CL interval on the inclusive signal strength modifier. The other panels show the measurements of the per production and decay channel signal strength modifiers, $ \mu^{if} $. Within these panels, the blue bands indicate the 68% CL intervals on the per production process signal strength modifiers. The SM predicted values are indicated by the red lines. The central values and 68% CL intervals for the $ \mu^{if} $ parameters are explicitly written in each panel of the plot. The $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ signal strengths are constrained to be nonnegative as indicated by the grey hatched boxes. Additionally, the $ \mathrm{WH} $, $ \mathrm{ZH} $, and $ \mathrm{ttH}+\mathrm{tH} $ production processes for the $ \mathrm{H}\to\mathrm{Z}\gamma $ channel are constrained to the SM predictions, a feature that is indicated by the black hatched boxes. |
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Figure 7:
The correlations between the 31 parameters considered in the per production and decay channel fit. The size of the correlations is indicated by the colour scale. Correlations with an absolute magnitude smaller than 0.005 are not shown. |
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Figure 8:
The measured STXS stage 0 cross sections and branching fraction ratios. Theoretical uncertainties affecting the normalizations of the measured parameters are not included in the fit. In the upper plot, the empty circles indicate the best fit values and the vertical lines with caps indicate the 68% CL intervals. The lower 68% CL interval for the $ \sigma^{\mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}}\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ parameter lies outside of the plotted range, as indicated by the arrow. The wider boxes show the systematic uncertainty components of the 68% CL intervals. Each measured quantity is compared with the SM prediction in red, where the grey bands indicate the theoretical uncertainty in the respective prediction. The lower plot shows the correlations between the 13 parameters considered in the fit. The size of the correlations is indicated by the colour scale. |
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Figure 8-a:
The measured STXS stage 0 cross sections and branching fraction ratios. Theoretical uncertainties affecting the normalizations of the measured parameters are not included in the fit. In the upper plot, the empty circles indicate the best fit values and the vertical lines with caps indicate the 68% CL intervals. The lower 68% CL interval for the $ \sigma^{\mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}}\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ parameter lies outside of the plotted range, as indicated by the arrow. The wider boxes show the systematic uncertainty components of the 68% CL intervals. Each measured quantity is compared with the SM prediction in red, where the grey bands indicate the theoretical uncertainty in the respective prediction. The lower plot shows the correlations between the 13 parameters considered in the fit. The size of the correlations is indicated by the colour scale. |
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Figure 8-b:
The measured STXS stage 0 cross sections and branching fraction ratios. Theoretical uncertainties affecting the normalizations of the measured parameters are not included in the fit. In the upper plot, the empty circles indicate the best fit values and the vertical lines with caps indicate the 68% CL intervals. The lower 68% CL interval for the $ \sigma^{\mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}}\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ parameter lies outside of the plotted range, as indicated by the arrow. The wider boxes show the systematic uncertainty components of the 68% CL intervals. Each measured quantity is compared with the SM prediction in red, where the grey bands indicate the theoretical uncertainty in the respective prediction. The lower plot shows the correlations between the 13 parameters considered in the fit. The size of the correlations is indicated by the colour scale. |
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Figure 9:
A diagram showing the set of 32 STXS regions that are considered. The filled boxes represent the measured STXS regions, while the dashed lines indicate the nominal STXS stage 1.2 bin boundaries that are merged in the measurement. The units of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ are in GeV. |
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Figure 10:
The measured STXS stage 1.2 cross sections and branching fraction ratios. Theoretical uncertainties that affect the normalizations of the measured parameters are not included in the fit. In the upper panel, the points indicate the best fit values while the coloured lines indicate the 68% CL intervals. The wider boxes show the systematic uncertainty components of the 68% CL intervals. Each measured quantity is compared to the SM prediction in red, where the grey bands indicate the theoretical uncertainty for the respective parameter. The lower panel plots the ratio of the measured $ \sigma^i\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ with respect to the SM predictions. The best fit values for the $ \mathrm{ggH} $ 450 $ < p_{\mathrm{T}}^{\mathrm{H}} < $ 650 GeV and $ \mathrm{tH} $ STXS bins lie outside of the range of the ratio panel, and are thus represented by arrows. Arrows are also used to indicate 68% CL intervals that extend beyond the plotted range. |
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Figure 11:
The correlations between the 36 parameters considered in the STXS stage 1.2 measurement. The size of the correlations is indicated by the colour scale. Correlations of absolute magnitude smaller than 0.005 are not shown. |
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Figure 12:
The best fit values (empty circles) and 68% CL intervals (coloured lines) for the measurement of the products of the cross sections and branching fractions. Theoretical uncertainties affecting the cross section normalizations and branching fractions are included in the fit. The best fit values for the products of cross sections and branching fractions are obtained by multiplying the fit parameters $ \mu^{if} $ by the SM predictions at the highest available order. Different panels show the measurements for the different Higgs boson decay channels. The ($ \mathrm{ttH} p_{\mathrm{T}}^{\mathrm{H}} > $ 300 GeV, $ \mathrm{H}\to\mathrm{b}\mathrm{b} $), ($ \mathrm{ggH} p_{\mathrm{T}}^{\mathrm{H}} > $ 300 GeV, $ \mathrm{H}\to\mathrm{W}\mathrm{W} $), and ($ \mathrm{ggH} $ 0J $ p_{\mathrm{T}}^{\mathrm{H}} < $ 10 GeV, $ \mathrm{H}\to\tau\tau $) best fit values and 68% CL intervals are entirely contained in the negative domain, and are represented by arrows as they cannot be shown on the log-scale axes. Arrows are also used to indicate 68% CL intervals that extend into the negative domain. The $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ parameters are restricted to nonnegative values, which is marked by the hatched grey lines in the corresponding panels. |
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Figure 13:
The coupling modifiers of the Higgs boson to fermions and gauge bosons, in the resolved coupling modifier measurement. In the left plot, the thick (thin) black lines indicate the 68% (95%) CL intervals around the best fit points (empty circles). For this model, both positive and negative values of $ \kappa_{\mathrm{W}} $, $ \kappa_{\mathrm{Z}} $, and $ \kappa_{\mathrm{b}} $ are considered, while $ \kappa_{\mathrm{t}} $ is restricted to the positive domain without loss of generality, as indicated by the hatched box. In the right plot, the measurements are shown as functions of the fermion or gauge boson mass, where $ v $ is the vacuum expectation value of the Brout-Englert-Higgs field. The 68% and 95% CL intervals are determined around the minimum that contains the best fit point. The b quark mass is evaluated at a scale equal to $ m_{\mathrm{H}} $. The uncertainties in the particle mass values are not shown in the figure. For gauge bosons, the square root of the coupling modifier is used to keep a linear proportionality to the mass, as predicted by the SM. |
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Figure 13-a:
The coupling modifiers of the Higgs boson to fermions and gauge bosons, in the resolved coupling modifier measurement. In the left plot, the thick (thin) black lines indicate the 68% (95%) CL intervals around the best fit points (empty circles). For this model, both positive and negative values of $ \kappa_{\mathrm{W}} $, $ \kappa_{\mathrm{Z}} $, and $ \kappa_{\mathrm{b}} $ are considered, while $ \kappa_{\mathrm{t}} $ is restricted to the positive domain without loss of generality, as indicated by the hatched box. In the right plot, the measurements are shown as functions of the fermion or gauge boson mass, where $ v $ is the vacuum expectation value of the Brout-Englert-Higgs field. The 68% and 95% CL intervals are determined around the minimum that contains the best fit point. The b quark mass is evaluated at a scale equal to $ m_{\mathrm{H}} $. The uncertainties in the particle mass values are not shown in the figure. For gauge bosons, the square root of the coupling modifier is used to keep a linear proportionality to the mass, as predicted by the SM. |
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Figure 13-b:
The coupling modifiers of the Higgs boson to fermions and gauge bosons, in the resolved coupling modifier measurement. In the left plot, the thick (thin) black lines indicate the 68% (95%) CL intervals around the best fit points (empty circles). For this model, both positive and negative values of $ \kappa_{\mathrm{W}} $, $ \kappa_{\mathrm{Z}} $, and $ \kappa_{\mathrm{b}} $ are considered, while $ \kappa_{\mathrm{t}} $ is restricted to the positive domain without loss of generality, as indicated by the hatched box. In the right plot, the measurements are shown as functions of the fermion or gauge boson mass, where $ v $ is the vacuum expectation value of the Brout-Englert-Higgs field. The 68% and 95% CL intervals are determined around the minimum that contains the best fit point. The b quark mass is evaluated at a scale equal to $ m_{\mathrm{H}} $. The uncertainties in the particle mass values are not shown in the figure. For gauge bosons, the square root of the coupling modifier is used to keep a linear proportionality to the mass, as predicted by the SM. |
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Figure 14:
The measured Higgs boson coupling modifiers in the effective coupling configuration. The best fit values, and 68% and 95% CL intervals, are shown for each of the models considered. The results assuming no additional BSM contributions to the Higgs boson total decay width are shown in blue. The results for the model that allows BSM contributions but places external constraints on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $ are shown in orange, with the constraints $ |\kappa_{\mathrm{W}}|,|\kappa_{\mathrm{Z}}| \leq $ 1 indicated by hatched boxes. The results for the fit in which the off-shell analysis regions are included are shown in purple. In all three models, both positive and negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $ are considered, while $ \kappa_{\mathrm{t}} $ is restricted to the positive domain without loss of generality, as indicated by a hatched box. The parameters $ \mathcal{B}_{\text{inv}} $ and $ \mathcal{B}_{\text{undet}} $, included in the latter two models, are defined to be nonnegative, which is likewise indicated by a hatched box. The arrows shown for $ \kappa_{\mathrm{Z}\gamma} $ are used to indicate 68% CL intervals that extend beyond the plotted range. |
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Figure 15:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-a:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-b:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-c:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-d:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-e:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 15-f:
Scans of the test statistic $ q $ as a function of $ \kappa_{\mathrm{W}} $ (left) and $ \kappa_{\mathrm{t}} $ (right) for the three effective coupling modifier models. The upper row shows the model that assumes no additional BSM contributions to the Higgs boson total decay width. The middle row shows the model that introduces BSM contributions, but places an external constraint on $ |\kappa_{\mathrm{W}}| $ and $ |\kappa_{\mathrm{Z}}| $, and the lower row shows the model in which the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ analysis regions are included. The different coloured lines indicate the value of $ q $ for different combinations of signs for $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. The solid black line shows the minimum value of $ q $ across all combinations of signs, which is used to determine the best fit point and the 68% and 95% CL intervals. The scan in the middle left plot is truncated because of the external constraint of $ |\kappa_{\mathrm{W}}| \leq $ 1, which is indicated by the hatched boxes. The plots in the lower row are shown on a different $ y $-axis scale to emphasize the exclusion of the sign combinations that include negative values of $ \kappa_{\mathrm{W}} $ and $ \kappa_{\mathrm{Z}} $. |
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Figure 16:
The measured parameters in the ratios of coupling modifiers fit. The thick (thin) black lines indicate the 68% (95%) CL intervals, around the best fit points (empty circles). For this model, both positive and negative values of $ \lambda_{\mathrm{W}\mathrm{Z}} $ and $ \lambda_{\mathrm{t}\mathrm{g}} $ are considered, while $ \kappa_{\mathrm{g}\mathrm{Z}} $ and $ \lambda_{\mathrm{Z}\mathrm{g}} $ are restricted to the positive domain without loss of generality, as indicated by the hatched box. |
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Figure 17:
The measured parameters in the fits probing the symmetry of fermion couplings. The left plot shows the results for the model that probes the ratio of couplings to up-type and down-type fermions. In this fit, both positive and negative values of $ \lambda_{\mathrm{d}\mathrm{u}} $ and $ \lambda_{\mathrm{V}\mathrm{u}} $ are considered. The right plot shows the results for the model that probes the ratio of couplings to leptons and quarks, where both positive and negative values of $ \lambda_{\mathrm{l}\mathrm{q}} $ and $ \lambda_{\mathrm{V}\mathrm{q}} $ are considered. In both plots, the thick (thin) black lines indicate the 68% (95%) CL intervals, around the best fit points (empty circles). The hatched boxes indicate parameters that are restricted to the positive domain. |
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Figure 17-a:
The measured parameters in the fits probing the symmetry of fermion couplings. The left plot shows the results for the model that probes the ratio of couplings to up-type and down-type fermions. In this fit, both positive and negative values of $ \lambda_{\mathrm{d}\mathrm{u}} $ and $ \lambda_{\mathrm{V}\mathrm{u}} $ are considered. The right plot shows the results for the model that probes the ratio of couplings to leptons and quarks, where both positive and negative values of $ \lambda_{\mathrm{l}\mathrm{q}} $ and $ \lambda_{\mathrm{V}\mathrm{q}} $ are considered. In both plots, the thick (thin) black lines indicate the 68% (95%) CL intervals, around the best fit points (empty circles). The hatched boxes indicate parameters that are restricted to the positive domain. |
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Figure 17-b:
The measured parameters in the fits probing the symmetry of fermion couplings. The left plot shows the results for the model that probes the ratio of couplings to up-type and down-type fermions. In this fit, both positive and negative values of $ \lambda_{\mathrm{d}\mathrm{u}} $ and $ \lambda_{\mathrm{V}\mathrm{u}} $ are considered. The right plot shows the results for the model that probes the ratio of couplings to leptons and quarks, where both positive and negative values of $ \lambda_{\mathrm{l}\mathrm{q}} $ and $ \lambda_{\mathrm{V}\mathrm{q}} $ are considered. In both plots, the thick (thin) black lines indicate the 68% (95%) CL intervals, around the best fit points (empty circles). The hatched boxes indicate parameters that are restricted to the positive domain. |
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Figure 18:
Profile likelihood ratio scans as functions of $ \kappa_\lambda $ for the observed data (solid lines). The expected results assuming an SM Higgs boson derived using an Asimov data set with $ \kappa_\lambda= $ 1 are shown by the dashed lines. The blue lines represent the case where $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $ are fixed to 1. The orange lines represent the case where $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $ are profiled. |
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Figure 19:
Profile likelihood ratio scans as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{F}} $ (upper) and as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{V}} $ (lower). The blue colour scale shows the value of $ q $ at each point in the scan. The black marker, and solid and dashed lines, show the best fit point, and the 68% and 95% CL contours, respectively. The red marker corresponds to the SM prediction. |
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Figure 19-a:
Profile likelihood ratio scans as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{F}} $ (upper) and as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{V}} $ (lower). The blue colour scale shows the value of $ q $ at each point in the scan. The black marker, and solid and dashed lines, show the best fit point, and the 68% and 95% CL contours, respectively. The red marker corresponds to the SM prediction. |
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Figure 19-b:
Profile likelihood ratio scans as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{F}} $ (upper) and as a function of $ \kappa_{\lambda} $ and $ \kappa_{\mathrm{V}} $ (lower). The blue colour scale shows the value of $ q $ at each point in the scan. The black marker, and solid and dashed lines, show the best fit point, and the 68% and 95% CL contours, respectively. The red marker corresponds to the SM prediction. |
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Figure 20:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 20-a:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 20-b:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 20-c:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 20-d:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 20-e:
Constraints in the $ \tan{\beta} $ vs. $ \cos{(\beta-\alpha)} $ plane for the Type-I, Type-II, lepton-specific, and Flipped 2HDM scenarios, and constraints in the $ \tan{\beta} $ vs. $ m_{\mathrm{A}} $ plane for the hMSSM scenario. The grey regions, bounded by the solid black lines, represent the regions of parameter space that are excluded at the 95% CL, given the data observed. The dashed black lines indicate the expected boundaries of the 95% CL exclusion regions, for an SM Higgs boson. The dashed red lines in the 2HDM plots indicate the alignment limit, $ \cos{(\beta-\alpha)}= $ 0, where the Higgs boson couplings coincide with the SM predictions. |
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Figure 21:
Impact of the SMEFT operators on the Higgs boson cross sections and branching fractions. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The impacts are shown for operators from the following groups: $ X^3 $, $ H^4D^2 $, $ X^2H^2 $, $ \psi^2H^3 $, and $ \psi^2XH $. The WCs are set to the expected symmetrized 95% CL interval value in the linear-plus-quadratic parametrization, assuming all other WCs are set to zero (SM). The impacts are shown relative to the SM predictions for the linear parametrization in the filled histograms, and the linear-plus-quadratic parametrization in the open histograms. |
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Figure 22:
Impact of the SMEFT operators on the Higgs boson production cross sections and branching fractions. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The impacts are shown for operators from the $ \psi^2H^2D $ group. The WCs are set to the expected symmetrized 95% CL interval value in the linear-plus-quadratic parametrization, assuming all other WCs are set to zero (SM). The impacts are shown relative to the SM predictions for the linear parametrization in the filled histograms, and the linear-plus-quadratic parametrization in the open histograms. |
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Figure 23:
Impact of the SMEFT operators on the Higgs boson production cross sections and branching fractions. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The impacts are shown for operators from the four-fermion groups. The WCs are set to the expected symmetrized 95% CL interval value in the linear-plus-quadratic parametrization, assuming all other WCs are set to zero (SM). The impacts are shown relative to the SM predictions for the linear parametrization in the filled histograms, and the linear-plus-quadratic parametrization in the open histograms. |
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Figure 24:
Individual constraints on the SMEFT WCs. The left panel shows the best fit values, and the 68% and 95% CL intervals, when considering modifications in one SMEFT operator at a time. The results from the linear and linear-plus-quadratic parametrizations are shown in blue and orange, respectively. Arrows are used to indicate where the 95% CL interval extends beyond the plotted range. In the right panel, the results are translated into a 95% lower limit on the BSM physics energy scale. The WCs are categorized into operators from the same group, and then listed in order of the probed energy scale using the linear-plus-quadratic parametrization. The hatched lines represent WCs that cannot be constrained in the linear-only parametrization. |
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Figure 25:
Truncated rotation matrix $ \mathcal{R} $, derived using the PCA procedure. Only the 17 eigenvectors that are included in the fit are shown. Each row represents a different eigenvector $ \mathrm{EV}_j $ ordered by constraining power. The left panel shows 1 $ /\sqrt{\lambda_j} $ for each eigenvector, where $ \lambda_j $ is the corresponding eigenvalue. This quantity provides an estimate of the expected 68% CL intervals. The vertical red line identifies the threshold beyond which the eigenvectors are not considered in the fit. The right panel shows the rotation matrix elements, $ \mathcal{R}_{jk} $, for each Wilson coefficient $ c_k $, such that $ \mathrm{EV}_j = \sum_k \mathcal{R}_{jk}c_k $. The size of each element is represented by a colour scale with red meaning large positive values and blue meaning large negative values. The value of each element is also shown in the plot. |
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Figure 26:
Impact of the eigenvectors $ \mathrm{EV}_j $ on the $ \mu^{if} $ parameters from the 97 POI fit (Fig. 12), for the $ \mathrm{H}\to\gamma\gamma $, $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $, $ \mathrm{H}\to\mu\mu $, and $ \mathrm{H}\to\mathrm{Z}\gamma\to\ell\ell\gamma $ decay channels. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The $ \mathrm{EV}_j $ are individually set to their expected symmetrized 95% CL interval value in the fully profiled fit. When varying one eigenvector, all other eigenvectors are set to zero (SM). The impacts are shown relative to the SM predictions for the linear parametrization. The eigenvectors are ordered from most sensitive (upper) to least sensitive (lower). All eigenvectors included in the fit are shown. |
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Figure 27:
Impact of the eigenvectors $ \mathrm{EV}_j $ on the $ \mu^{if} $ parameters from the 97 POI fit (Fig. 12), for the $ \mathrm{H}\to\mathrm{W}\mathrm{W}\to\ell\nu\ell\nu $, $ \mathrm{H}\to\tau\tau $, and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decay channels. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The $ \mathrm{EV}_j $ are individually set to their expected symmetrized 95% CL interval value in the fully profiled fit. When varying one eigenvector, all other eigenvectors are set to zero (SM). The impacts are shown relative to the SM predictions for the linear parametrization. The eigenvectors are ordered from most sensitive (upper) to least sensitive (lower). All eigenvectors included in the fit are shown. |
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Figure 28:
Constraints on the linear combinations of SMEFT WCs extracted with the PCA procedure. The left panel shows the observed best fit values, and 68% and 95% CL intervals, as well as the expected 95% CL intervals, for a linear parametrization with terms up to $ \mathcal{O}(\mathrm{EV}/\Lambda^2) $. An arrow is used to indicate where the 95% CL interval for $ \mathrm{EV}_{2} $ extends beyond the plotted range. In the right panel, the results are translated into a 95% lower limit on the BSM physics energy scale, assuming $ \mathrm{EV}_j = $ 1. The eigenvectors are listed in order of the expected excluded energy scale. |
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Figure 29:
Correlation matrix for the linear combinations of SMEFT WCs extracted with the PCA procedure. |
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Figure 30:
Comparison of the constraints on the linear combinations of SMEFT WCs for different fit strategies. The results shown in black are obtained using the full combination likelihood, and are the same as those shown in Fig. 28. The results in orange and red are obtained with a simplified likelihood procedure, constructed from the 97 POI fit to STXS measurements (result shown in Fig. 12). The results shown in orange are based on a symmetric uncertainty model, while the results shown in red account for asymmetric uncertainties. The left panel shows the observed best fit values, and 68% and 95% CL intervals, as well as the expected 95% CL intervals. In the right panel, the results are translated into a 95% CL lower limit on the BSM physics energy scale, assuming $ \mathrm{EV}_j = $ 1. The eigenvectors are listed in order of the expected excluded energy scale from the full likelihood fit. The fits use a linear SMEFT parametrization, in which terms up to $ \mathcal{O}(\mathrm{EV}/\Lambda^2) $ are included. |
| Tables | |
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Table 1:
Summary of the input analyses in the combination. The second column lists the final-state particles that are targeted in each analysis. Here, $ \tau_h $ indicates a hadronically decaying $ \tau $ lepton and $ p_{\mathrm{T}}^\text{miss} $ is the magnitude of the missing transverse momentum vector. The third column lists the production processes and STXS kinematic regions targeted in each analysis. The variables $ N $J, $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ refer to the jet multiplicity, the transverse momentum of the Higgs boson, the invariant mass of the two leading jets, the transverse momentum of the Higgs plus dijet system, and the transverse momentum of the vector boson, respectively. The fourth column indicates the granularity of the signal model used in each analysis. More information on each analysis can be found in the references listed in the last column. |
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Table 2:
A list of the different signal parametrization models provided in the combination, and the channels that are included in each fit. The first column indicates the number of POIs in the model. The last column indicates whether the model is included in this paper (no checkmark) or is provided as supplementary material (checkmark). The remaining columns show ticks for each channel entering the respective model fit. All input channels, except off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $, are labelled as ``incl.'' or ``STXS'' according to the granularity of the signal processes. As described in Section 3, the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ boosted, and $ \mathrm{ttH} $ ($ \mathrm{H}\to\mathrm{b}\mathrm{b} $) inputs implement two sets of analysis regions. |
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Table 3:
Best fit values and 68% CL intervals for the per production process and per decay channel signal strengths. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. |
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Table 4:
Best fit values and 68% CL intervals for the per production and decay channel signal strengths. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. Some of the signal strengths are restricted to nonnegative values, as described in the text. Truncated intervals are reported for these parameters if the 68% CL interval is not fully contained in the positive domain. |
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Table 5:
Best fit values and 68% CL intervals for the parameters in the fit of production process cross sections and branching fraction ratios. The cross sections are defined in the fiducial region $ |y_{\mathrm{H}}| < $ 2.5. The values are normalized to the SM predictions. The total 68% CL intervals are decomposed into their statistical and systematic components, and the expected intervals are given in parentheses. The SM predictions for each of the measured parameters are also provided, along with the corresponding theoretical uncertainties in the predictions. The $ \sigma^{\mathrm{ggH}}\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ prediction includes contributions from $ \mathrm{bbH} $ production and $ \mathrm{ggZH} $ production with the Z boson decaying to hadrons, while $ \sigma^{\mathrm{Z}(\ell\ell,\nu\nu)\mathrm{H}}\mathcal{B}^{\mathrm{Z}\mathrm{Z}} $ includes contributions from $ \mathrm{ggZH} $ production with the Z boson decaying to leptons. |
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Table 6:
A summary of the STXS regions measured in the combination. All STXS regions are defined within the fiducial region $ |y_{\mathrm{H}}| < $ 2.5. Some of the measured regions are defined by merging several neighbouring bins (in parentheses) from the nominal STXS stage 1.2 binning scheme to ensure sufficient sensitivity. The SM predictions for the measured STXS regions are also provided. Units of GeV are assumed for all numerical values related to the $ p_{\mathrm{T}}^{\mathrm{H}} $, $ m_{\mathrm{jj}} $, $ p_{\mathrm{T}}^{\mathrm{H}\mathrm{jj}} $, and $ p_{\mathrm{T}}^\mathrm{V} $ variables. The $ \mathrm{ggH} $ ($ \mathrm{ZH} $ lep) bins include contributions from $ \mathrm{ggZH} $ production with the Z boson decaying hadronically (leptonically). The ``$ \mathrm{VBF} $-topo'' or ``$ \mathrm{VH} $-topo'' naming convention refers to events consistent with the topology of $ \mathrm{VBF} $ or $ \mathrm{VH} $ production, characterized by two jets with large $ m_{\mathrm{jj}} $ (for VBF), or two jets with $ m_{\mathrm{jj}} $ compatible with a vector boson decay (for $ \mathrm{VH} $). |
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Table 7:
Best fit values and 68% CL intervals for the parameters in the fit to stage 1.2 simplified template cross sections and branching fraction ratios. The cross sections are defined in the fiducial region $ |y_{\mathrm{H}}| < $ 2.5. The values are normalized to the SM predictions. The total 68% CL intervals are decomposed into their statistical and systematic components, and the expected intervals are given in parentheses. The SM prediction, with its theoretical uncertainty, for each of the measured parameters is also provided. |
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Table 8:
Best fit values and 68% CL intervals for the fit that introduces a separate POI for each STXS bin in each decay channel. The cross sections are defined in the fiducial region $ |y_{\mathrm{H}}| < $ 2.5. The values are normalized to the SM predictions. The fit is performed in the signal strength formalism, such that the theoretical uncertainties in the SM predictions are folded into the measurement. The expected intervals are given in parentheses. Some of the parameters are restricted to nonnegative values, as described in the text. Truncated intervals are reported for these parameters if the 68% CL interval is not fully contained in the positive domain. |
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Table 9:
Normalization scaling factors for all relevant production cross sections, partial decay widths, and the total Higgs boson decay width. For the $ \kappa $ parameters representing loop processes, the resolved scaling in terms of the fundamental SM couplings is also given. Only the dominant terms in the resolved scaling factor functions are provided in the table. The contributions are calculated for $ m_{\mathrm{H}} = $ 125.38 GeV. |
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Table 10:
Best fit values and 68% CL intervals for the Higgs boson coupling modifiers in the resolved coupling configuration. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. |
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Table 11:
Best fit values and 68% CL intervals for the Higgs boson coupling modifiers in the effective coupling configuration. The results are shown for each of the models considered. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. The one-sided intervals represent physical boundaries in the POIs. |
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Table 12:
Best fit values and 68% CL intervals for the coupling modifier ratios. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. |
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Table 13:
Best fit values and 68% CL intervals for the three parameter models that probe the symmetry of fermion couplings. The total 68% CL intervals are decomposed into their statistical and systematic components. The expected intervals are given in parentheses. |
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Table 14:
Best fit values, 68% CL, and 95% CL intervals for $ \kappa_\lambda $, with different assumptions on the values of $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $. The expected intervals are given in parentheses. The $ p_{\text{SM}} $ values, which represent the compatibility with the SM hypothesis, are also provided. A 95% CL interval for the fit in which $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $ are floating cannot be extracted within the range of validity for this model. |
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Table 15:
Best fit values, 68% CL, and 95% CL intervals for $ \kappa_\lambda $, with different assumptions on the values of $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $. The expected intervals are given in parentheses. The $ p_{\text{SM}} $ values, which represent the compatibility with the SM hypothesis, are also provided. A 95% CL interval for the fit in which $ \kappa_{\mathrm{F}} $ and $ \kappa_{\mathrm{V}} $ are floating cannot be extracted within the range of validity for this model. |
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Table 16:
Modifications to the couplings of the Higgs boson to vector bosons, up-type quarks, down-type quarks, and charged leptons, in the 2HDM and hMSSM scenarios. The modifications act as multiplicative factors to the SM expectations. The expressions for $ s_{\mathrm{u}} $ and $ s_{\mathrm{d}} $, which enter the hMSSM terms, are given in Eqs. \eqrefeq:hmssm_su and \eqrefeq:hmssm_sd, respectively. |
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Table 17:
A list of the 43 WCs, $ c_j $, considered in the SMEFT interpretation, and the corresponding dimension-6 operators $ \mathcal{O}_j $. The coefficients are grouped into terms of a similar structure in the SM Lagrangian expansion. The operators follow the same notation as Ref. [109], where $ (q,u,d) $ denote the quark fields of the first two generations, $ (Q,t,b) $ quark fields of the third generation, and $ (\ell,e,\nu) $ lepton fields of all three generations. The Higgs doublet is represented by $ H $, a covariant derivative by $ D $, and a vector boson field by $ X=G,W,B $. Fermion fields are represented by $ \psi $, with $ L $ ($ R $) indicating left-handed (right-handed) fermion fields. The d'Alembertian operator is denoted by $ \Box $. |
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Table 18:
Expected and observed 95% CL intervals on the WCs, when considering modifications to one WC at a time. The results for both the linear and linear-plus-quadratic parametrisations are provided. Only the 95% CL intervals that contain the best fit points are reported. The best fit values and $ p_{\text{SM}} $ values are also given. |
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Table 19:
Expected and observed 95% CL intervals on the linear combinations of SMEFT WCs. The results are provided for the linear parametrisation. The best fit values are also given. |
| Summary |
| The most comprehensive combined measurements of Higgs boson (H) production and decay rates performed by the CMS Collaboration to date are reported. The combination uses proton-proton collision data recorded by the CMS experiment at $ \sqrt{s}= $ 13 TeV between 2016 and 2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The decay channels included in the combined measurements are $ \mathrm{H}\to\gamma\gamma $, $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $, $ \mathrm{H}\to\mathrm{W}\mathrm{W}\to\ell\nu\ell\nu $, $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\mathrm{b}\mathrm{b} $, $ \mathrm{H}\to\mu\mu $, and $ \mathrm{H}\to\mathrm{Z}\gamma\to\ell\ell\gamma $ ($ \ell=\mathrm{e} $ or $ \mu $). Information in the events from each decay channel is used to target several Higgs boson production processes. Results are provided for various assumptions on the scaling behaviour of Higgs boson production and decay. This includes measurements of signal strengths, production cross sections, branching fractions, and, for the first time, a combined measurement by the CMS Collaboration of kinematic regions defined by the simplified template cross section (STXS) framework. The inclusive signal strength is measured to be 1.014 $ ^{+0.055}_{-0.053} $ times the standard model (SM) expectation, for a Higgs boson mass of 125.38 GeV, where the largest contribution to the total uncertainty originates from the theoretical systematic component. The per production process signal strengths show a small tension with the SM ($ p_{\text{SM}} = $ 0.02), which is mainly driven by the observed excess of 2.2 standard deviations in the $ \mathrm{tH} $ production process. The corresponding 68% confidence level (CL) intervals range from 7.5% for gluon fusion ($ \mathrm{ggH} $) production to 39% for Higgs boson production in association with a top quark ($ \mathrm{tH} $), relative to the best fit value. The per decay channel signal strengths exhibit a good level of compatibility with the SM, with a $ p $-value of $ p_{\text{SM}} = $ 0.33. The 68% CL intervals range from 8% for $ \mathrm{H}\to\gamma\gamma $ to 39% for $ \mathrm{H}\to\mathrm{Z}\gamma $. Production cross section measurements are performed at two levels of granularity. The STXS stage 0 measurements correspond to the different Higgs boson production processes, while the STXS stage 1.2 measurements further partition the phase space into nonoverlapping kinematic regions. In total, 32 kinematic regions are measured simultaneously, of which 13 are associated with $ \mathrm{ggH} $ production, five with vector boson fusion production, four with each of W ($ \mathrm{WH} $) and Z ($ \mathrm{ZH} $) boson-associated production, where the vector boson decays leptonically, five with Higgs boson production in association with a top quark pair, and one with $ \mathrm{tH} $ production. The production cross sections are extracted as products with the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ branching fraction, and the ratios of branching fractions are included as additional parameters in the fit to account for modifications to the SM Higgs boson decay rates. Overall, the STXS stage 1.2 measurements show reasonable agreement with the SM predictions ($ p_{\text{SM}} = $ 0.06), with some tensions observed in the high transverse momentum ($ p_{\mathrm{T}}^\mathrm{V} $) regions of the $ \mathrm{WH} $ and $ \mathrm{ZH} $ leptonic production processes, as well as for $ \mathrm{tH} $ production. The 68% CL intervals relative to the SM predicted values range from $ \sim $14% for the $ \mathrm{ggH} $ STXS bin with no additional jets and Higgs boson transverse momentum between 10 and 200 GeV to $ \sim $260% for the $ \mathrm{ggH} $ STXS bin with Higgs boson transverse momentum greater than 650 GeV. A measurement considering a separate parameter for each STXS bin in each decay channel is also performed. In total 97 parameters are fitted, which constitutes the most granular measurement of the Higgs boson ever performed by the CMS Collaboration. Several interpretations of the measurements are also provided. Higgs boson coupling modifiers are probed in the $ \kappa $-framework for both the resolved and effective configurations. In the resolved coupling modifier configuration, the measurements exhibit a good level of compatibility with the SM ($ p_{\text{SM}} = $ 0.12). The vector boson and third generation fermion coupling modifiers are measured with 68% CL intervals ranging from 6% for $ \kappa_\mathrm{W} $ to 12% for $ \kappa_\mathrm{b} $. The Higgs boson coupling modifier to muons is measured with a 68% CL interval of 20%. Models with different assumptions on the total Higgs boson decay width are provided for the effective coupling modifier configuration, including models with beyond-the-SM (BSM) decays of the Higgs boson. In order to constrain the branching fraction to invisible final states that are allowed in BSM models, analyses targeting the $ \mathrm{H}\to\mathrm{inv} $ decay are included. One model also includes off-shell analysis regions in the combination to provide a constraint on the total Higgs boson decay width directly from data. In this fit, the invisible (undetected) branching fraction is constrained to be less than 13% (25%) at the 95% CL. Ratios of coupling modifiers are also extracted, including models that test the symmetry of the couplings of the Higgs boson to fermions. These models are further used to extract constraints on specific extensions of the SM that contain a second Higgs doublet. No significant deviations from the SM are observed and the allowed parameter spaces are significantly reduced with respect to previous indirect constraints from CMS. In addition, constraints on the trilinear Higgs boson self-coupling are provided. These constraints arise from next-to-leading order electroweak corrections to the Higgs boson production and decay rates. Assuming other Higgs boson couplings are as predicted in the SM, the trilinear self-coupling is measured to be 2.14 $ ^{+3.95}_{-3.16} $, relative to the SM prediction. An interpretation in the SM effective field theory (SMEFT) framework is also performed. This framework provides a model-agnostic tool to indirectly probe BSM physics via measurements of Higgs boson production and decay, assuming that the new particles of the BSM theory exist at an energy scale larger than the electroweak scale. A SMEFT parametrization of STXS measurements is derived using simulation. Individual constraints are extracted on the 43 SMEFT Wilson coefficients to which the combination is sensitive. To assess the compatibility of data with the SM, a $ p $-value is computed for each of the Wilson coefficients. These $ p $-values generally indicate good agreement with the SM predictions, with the majority being above 0.1. The largest discrepancy from the SM is observed in the $ c^{(3)}_{Hq} $ parameter ($ p_{\text{SM}} = $ 0.01), which is driven by the observed excesses in the high-$ p_{\mathrm{T}}^\mathrm{V} \mathrm{WH} $ and $ \mathrm{ZH} $ leptonic STXS measurements. In addition, simultaneous constraints are provided on linear combinations of SMEFT operators, where the constrained directions in parameter space are extracted using a principal component analysis procedure. A total of 17 independent directions in SMEFT parameter space are constrained, and the measurements show reasonable compatibility with the SM hypothesis ($ p_{\text{SM}} = $ 0.11). In conclusion, the results show good compatibility with the SM predictions for the majority of the measured parameters. |
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