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| CMS-PAS-HIG-23-013 | ||
| Combination and interpretation of fiducial differential Higgs boson production cross sections at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 22 July 2024 | ||
| Abstract: The Higgs boson fiducial differential production cross sections are sensitive probes for the presence of physics beyond the standard model. New physics may contribute to the gluon-gluon fusion loop, the dominant Higgs boson production mechanism at the LHC, and manifest itself as deviations from the expected standard model distributions. In this work we measure combined spectra from measurements performed in four of the dominant Higgs decay channels ($ \gamma\gamma $, ZZ, WW, $ \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 combined spectra provided are extrapolated to the full phase space. The fiducial measurements are then used to compute limits on Higgs couplings using the $ \kappa $-framework and the standard model effective field theory. | ||
| Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. 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 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. |
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Figure 1-a:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. 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 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. |
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Figure 1-b:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. 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 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. |
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Figure 1-c:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. 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 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. |
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Figure 1-d:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. 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 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. |
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Figure 2:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. 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 normalized by the bin width of the last but one bin. |
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Figure 2-a:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. 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 normalized by the bin width of the last but one bin. |
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Figure 2-b:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. 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 normalized by the bin width of the last but one bin. |
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Figure 2-c:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. 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 normalized by the bin width of the last but one bin. |
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Figure 3:
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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 3-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 3-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 4:
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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 4-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 4-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 5:
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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 5-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 5-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 implemented as nuisance parameters with no dependence on the BR, referred to as ``floating branching fractions'' in the text (right). The 68% and 95% CL contours are shown in solid and dashed lines respectively: the black ones are for observed data, the yellow ones for expected. The shading indicates the expected negative log-likelihood, with the scale shown on the right-hand side of the plots. |
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Figure 6:
Observed and expected two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra in all decay channels. |
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Figure 6-a:
Observed and expected two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra in all decay channels. |
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Figure 6-b:
Observed and expected two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra in all decay channels. |
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Figure 6-c:
Observed and expected two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra in all decay channels. |
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Figure 6-d:
Observed and expected two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra in all decay channels. |
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Figure 7:
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 to each decay channel is equal to 100. |
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Figure 8:
Graphical representation of the ten eigenvectors with the highest eigenvalues of the expected combined Fisher information matrix in SMEFT basis. Values lower than $ 10^{-3} $ are not shown. |
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Figure 9:
Summary of observed and expected confidence intervals at 68% and 95% confidence level (CL) for the first ten eigenvectors. Where a power of ten is shown, the value on the x-axis is multiplied by the corresponding power of ten. The eigenvectors are ordered by decreasing eigenvalue. |
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Figure 10:
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. |
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Figure 11:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $, $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $, and $ \mathrm{H} \rightarrow \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. The rightmost bins of the distributions are overflow bins, and normalized by the bin width of last but one bin. |
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Figure 11-a:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $, $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $, and $ \mathrm{H} \rightarrow \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. The rightmost bins of the distributions are overflow bins, and normalized by the bin width of last but one bin. |
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Figure 11-b:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $, $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $, and $ \mathrm{H} \rightarrow \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. The rightmost bins of the distributions are overflow bins, and normalized by the bin width of last but one bin. |
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Figure 11-c:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $, $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $, and $ \mathrm{H} \rightarrow \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. The rightmost bins of the distributions are overflow bins, and normalized by the bin width of last but one bin. |
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Figure 11-d:
Measurement of the total differential cross section as a function of $ p_{\mathrm{T}}^{\mathrm{H}} $, $ N_{\mathrm{jets}} $, $ p_{\mathrm{T}}^{\mathrm{j}_1} $ and $ |y_{\mathrm{H}}| $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $, $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $, and $ \mathrm{H} \rightarrow \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. The rightmost bins of the distributions are overflow bins, and normalized by the bin width of last but one bin. |
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Figure 12:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 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 normalized by the bin width of last but one bin. |
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Figure 12-a:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 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 normalized by the bin width of last but one bin. |
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Figure 12-b:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 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 normalized by the bin width of last but one bin. |
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Figure 12-c:
Measurement of the total differential cross section as a function of $ |\Delta\eta_{\mathrm{jj}}| $, $ m_{\mathrm{jj}} $ and $ \tau^{\mathrm{j}}_{\mathrm{C}} $. The combined spectrum is shown in black points with error bars indicating a 1 standard deviation uncertainty. The systematic component of the uncertainty is shown in gray. The spectra for the $ \mathrm{H} \rightarrow \gamma \gamma $, and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 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 normalized by the bin width of last but one bin. |
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Figure 13:
Bin-to-bin correlation matrices for the $ p_{\mathrm{T}}^{\mathrm{H}} $ (top left), $ N_{\mathrm{jets}} $ (top right), $ |y_{\mathrm{H}}| $ (bottom left) and $ p_{\mathrm{T}}^{\mathrm{j}_1} $ (bottom right) spectra. |
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Figure 13-a:
Bin-to-bin correlation matrices for the $ p_{\mathrm{T}}^{\mathrm{H}} $ (top left), $ N_{\mathrm{jets}} $ (top right), $ |y_{\mathrm{H}}| $ (bottom left) and $ p_{\mathrm{T}}^{\mathrm{j}_1} $ (bottom right) spectra. |
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Figure 13-b:
Bin-to-bin correlation matrices for the $ p_{\mathrm{T}}^{\mathrm{H}} $ (top left), $ N_{\mathrm{jets}} $ (top right), $ |y_{\mathrm{H}}| $ (bottom left) and $ p_{\mathrm{T}}^{\mathrm{j}_1} $ (bottom right) spectra. |
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Figure 13-c:
Bin-to-bin correlation matrices for the $ p_{\mathrm{T}}^{\mathrm{H}} $ (top left), $ N_{\mathrm{jets}} $ (top right), $ |y_{\mathrm{H}}| $ (bottom left) and $ p_{\mathrm{T}}^{\mathrm{j}_1} $ (bottom right) spectra. |
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Figure 13-d:
Bin-to-bin correlation matrices for the $ p_{\mathrm{T}}^{\mathrm{H}} $ (top left), $ N_{\mathrm{jets}} $ (top right), $ |y_{\mathrm{H}}| $ (bottom left) and $ p_{\mathrm{T}}^{\mathrm{j}_1} $ (bottom right) spectra. |
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Figure 14:
Bin-to-bin correlation matrices for the $ m_{\mathrm{jj}} $ (top left), $ |\Delta\eta_{\mathrm{jj}}| $ (top right) and $ \tau^{\mathrm{j}}_{\mathrm{C}} $ (bottom) spectra. |
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Figure 14-a:
Bin-to-bin correlation matrices for the $ m_{\mathrm{jj}} $ (top left), $ |\Delta\eta_{\mathrm{jj}}| $ (top right) and $ \tau^{\mathrm{j}}_{\mathrm{C}} $ (bottom) spectra. |
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Figure 14-b:
Bin-to-bin correlation matrices for the $ m_{\mathrm{jj}} $ (top left), $ |\Delta\eta_{\mathrm{jj}}| $ (top right) and $ \tau^{\mathrm{j}}_{\mathrm{C}} $ (bottom) spectra. |
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Figure 14-c:
Bin-to-bin correlation matrices for the $ m_{\mathrm{jj}} $ (top left), $ |\Delta\eta_{\mathrm{jj}}| $ (top right) and $ \tau^{\mathrm{j}}_{\mathrm{C}} $ (bottom) spectra. |
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Figure 15:
Two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ \Delta\phi_{\mathrm{jj}} $ spectra in $ \mathrm{H} \rightarrow \gamma \gamma $ and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $. |
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Figure 15-a:
Two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ \Delta\phi_{\mathrm{jj}} $ spectra in $ \mathrm{H} \rightarrow \gamma \gamma $ and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $. |
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Figure 15-b:
Two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ \Delta\phi_{\mathrm{jj}} $ spectra in $ \mathrm{H} \rightarrow \gamma \gamma $ and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $. |
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Figure 15-c:
Two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ \Delta\phi_{\mathrm{jj}} $ spectra in $ \mathrm{H} \rightarrow \gamma \gamma $ and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $. |
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Figure 15-d:
Two dimensional scans for the $ c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}} $ (top left), $ c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}} $ (top right), $ c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}} $ (bottom left) and $ c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}} $ (bottom right) pairs with $ \Delta\phi_{\mathrm{jj}} $ spectra in $ \mathrm{H} \rightarrow \gamma \gamma $ and $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $. |
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Figure 16:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-a:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-b:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-c:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-d:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-e:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-f:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-g:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-h:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-i:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
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Figure 16-j:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-k:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-l:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-m:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-n:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-o:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 16-p:
Expected and observed profile likelihood scans for the first part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-a:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-b:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-c:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-d:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-e:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-f:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-g:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-h:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-i:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-j:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-k:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-l:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-m:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-n:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 17-o:
Expected and observed profile likelihood scans for the second part of the set of Wilson coefficients used as input to the PCA procedure. The scans are performed for the full combination of $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra. In each case, the other Wilson coefficients are set to their SM values. |
png pdf |
Figure 18:
Summary of observed and expected confidence intervals at 68% and 95% confidence level (CL) for the Wilson coefficients used as input to the PCA procedure. Where a power of ten is shown, the value on the x-axis is multiplied by the corresponding power of ten. |
png pdf |
Figure 19:
Observed and expected profile likelihood scans for eigenvectors 0 to 3. |
png pdf |
Figure 19-a:
Observed and expected profile likelihood scans for eigenvectors 0 to 3. |
png pdf |
Figure 19-b:
Observed and expected profile likelihood scans for eigenvectors 0 to 3. |
png pdf |
Figure 19-c:
Observed and expected profile likelihood scans for eigenvectors 0 to 3. |
png pdf |
Figure 19-d:
Observed and expected profile likelihood scans for eigenvectors 0 to 3. |
png pdf |
Figure 20:
Observed and expected profile likelihood scans for eigenvectors 4 to 7. |
png pdf |
Figure 20-a:
Observed and expected profile likelihood scans for eigenvectors 4 to 7. |
png pdf |
Figure 20-b:
Observed and expected profile likelihood scans for eigenvectors 4 to 7. |
png pdf |
Figure 20-c:
Observed and expected profile likelihood scans for eigenvectors 4 to 7. |
png pdf |
Figure 20-d:
Observed and expected profile likelihood scans for eigenvectors 4 to 7. |
png pdf |
Figure 21:
Observed and expected profile likelihood scans for eigenvectors 8 and 9. |
png pdf |
Figure 21-a:
Observed and expected profile likelihood scans for eigenvectors 8 and 9. |
png pdf |
Figure 21-b:
Observed and expected profile likelihood scans for eigenvectors 8 and 9. |
| Tables | |
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Table 1:
$ p_T^H $ bin boundaries used in the combination. |
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Table 2:
$ N_{jets} $ bins used in the combination. |
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Table 3:
$ p_{\mathrm{T}}^{\mathrm{j}_1} $ bin boundaries used in the combination. |
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Table 4:
$ |y_{\mathrm{H}}| $ bin boundaries used in the combination. |
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Table 5:
$ |\Delta\eta_{\mathrm{jj}}| $ bin boundaries used in the combination. |
png pdf |
Table 6:
$ m_{\mathrm{jj}} $ bin boundaries used in the combination. |
png pdf |
Table 7:
$ \tau^{\mathrm{j}}_{\mathrm{C}} $ bin boundaries used in the combination. |
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Table 8:
$ |\Delta\phi _{\mathrm{jj}}| $ ($ \mathrm{H} \rightarrow \gamma \gamma $) and $ \Delta\phi _{\mathrm{jj}} $ ($ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $) boundaries used for fits to Wilson coefficients. |
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Table 9:
List of $ X^2H^2 $ operators and corresponding Wilson coefficients. On the rightmost column, example diagrams of the processes affected by the operators are shown. |
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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 11:
Observed best fit differential cross section for the $ p_{\mathrm{T}}^{H} $ [GeV] observable |
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Table 12:
Observed best fit differential cross section for the $ N_{jets} $ observable |
png pdf |
Table 13:
Observed best fit differential cross section for the $ y_{H} $ observable |
png pdf |
Table 14:
Observed best fit differential cross section for the $ p_{\mathrm{T}}^{jet} $ [GeV] observable |
png pdf |
Table 15:
Observed best fit differential cross section for the $ m _{\mathrm{jj}} $ [GeV] observable |
png pdf |
Table 16:
Observed best fit differential cross section for the $ \Delta\eta _{\mathrm{jj}} $ observable |
png pdf |
Table 17:
Observed best fit differential cross section for the $ \tau_{C}^{j} $ [GeV] observable |
| Summary |
| A combination of differential cross sections for the differential 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}} $ is presented, using 138 fb$^{-1}$ of proton-proton collision data obtained at $ \sqrt{s} = $ 13 TeV. The obtained spectra are obtained on data from the $ \mathrm{H} \rightarrow \gamma \gamma $, $ \mathrm{H} \rightarrow \mathrm{Z} \mathrm{Z}^{(*)} \rightarrow 4\ell $, $ \mathrm{H} \rightarrow \mathrm{W^+} \mathrm{W^-}^{(*)} \rightarrow \mathrm{e}^{\pm} \mu^{\mp} \nu_{l} \overline{\nu}_{l} $ and $ \mathrm{H} \rightarrow \tau^{+} \tau^{-} $ (boosted and not). No significant deviations from the standard model predictions are observed in any differential distribution. The obtained $ p_{\mathrm{T}}^{\mathrm{H}} $ spectra were interpreted using the $ \kappa $-framework and the SMEFT framework: in the former, multiple couplings were varied simultaneously following the studies reported in [10], while in the latter a principal component analysis was performed to identify non-flat directions of the likelihood. In both cases, the results are compatible with the standard model predictions. |
| Additional Figures | |
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Additional Figure 1:
The 95% confidence level (CL) limits for each Wilson coefficient $ c_i $, obtained while setting the others to their SM value, interpreted in terms of the energy scale $ \Lambda $ for three different assumptions for the value of the coefficient as indicated in the legend. For limits that are not symmetrical around the SM value of zero, the absolute value of the looser limit is used. |
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Additional Figure 2:
The 95% CL profiled limits for the ten eigenvectors (EVs) with highest eigenvalues, interpreted in terms of the energy scale $ \Lambda $ for three different assumptions for the value of the coefficient as indicated in the legend. For limits that are not symmetrical around the SM value of zero, the absolute value of the looser limit is used. |
png pdf |
Additional Figure 3:
Summary plot of the impacts of the different analysis $ p_{\mathrm{T}}^{\mathrm{H}} $ bins on the fitted eigenvectors obtained by the PCA. The choice of the different values for which the impacts are shown is chosen to be the observed 95% CL limit. The value of $ \mu(c_i) $ is computed by substituting the previously mentioned value of $ c_i $ into the linearized parametrization while leaving all the other eigenvectors fixed to their SM value. |
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Compact Muon Solenoid LHC, CERN |
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