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| CMS-PAS-HIG-24-004 | ||
| Model-independent measurement of the Higgs boson differential production cross section in association with two jets in the WW decay channel | ||
| CMS Collaboration | ||
| 7 April 2025 | ||
| Abstract: A model-independent measurement is presented of the differential production cross section of the Higgs boson decaying into a pair of W bosons, with a final state including two jets. The analysis selects events where the decay products of the two W bosons consist of an electron, a muon, and two neutrinos. The study is based on proton-proton collision data collected by the CMS detector from 2016 to 2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The production cross sections are measured as a function of the difference in azimuthal angle between the two jets. The differential cross section measurements are further used to constrain Higgs boson couplings within the SM effective field theory framework. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Normalized distribution of the VBF differential cross section as a function of the signed azimuthal angle difference between the two VBF jets for a Higgs boson mass of 125 GeV, assuming a mixed CP scenario, a pure CP-even or CP-odd AC, and the SM coupling in the HVV vertex. |
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Figure 2:
Normalized distributions of $ \mathcal{D}_\mathrm{VBF}\ $ (left) and $ \mathcal{D}_\mathrm{ggF}\ $ (right), evaluated on signal and background events. The signal is displayed for the different physics hypotheses, with the SM contribution represented by dots and associated error bars reflecting the statistical uncertainty, and alternative hypotheses in solid lines. |
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Figure 2-a:
Normalized distributions of $ \mathcal{D}_\mathrm{VBF}\ $ (left) and $ \mathcal{D}_\mathrm{ggF}\ $ (right), evaluated on signal and background events. The signal is displayed for the different physics hypotheses, with the SM contribution represented by dots and associated error bars reflecting the statistical uncertainty, and alternative hypotheses in solid lines. |
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Figure 2-b:
Normalized distributions of $ \mathcal{D}_\mathrm{VBF}\ $ (left) and $ \mathcal{D}_\mathrm{ggF}\ $ (right), evaluated on signal and background events. The signal is displayed for the different physics hypotheses, with the SM contribution represented by dots and associated error bars reflecting the statistical uncertainty, and alternative hypotheses in solid lines. |
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Figure 3:
Response matrix of the fiducial component of the SM VBF (left) and ggF (right) signal, constructed using the 2018 data set. Each column is normalized to 1. |
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Figure 3-a:
Response matrix of the fiducial component of the SM VBF (left) and ggF (right) signal, constructed using the 2018 data set. Each column is normalized to 1. |
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Figure 3-b:
Response matrix of the fiducial component of the SM VBF (left) and ggF (right) signal, constructed using the 2018 data set. Each column is normalized to 1. |
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Figure 4:
Post-fit $ \mathcal{D}_\mathrm{VBF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. A uniform binning is applied for visualization, with the true binning range indicated on the x-axis. The binning scheme optimized for the 2018 data set is used. |
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Figure 4-a:
Post-fit $ \mathcal{D}_\mathrm{VBF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. A uniform binning is applied for visualization, with the true binning range indicated on the x-axis. The binning scheme optimized for the 2018 data set is used. |
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Figure 4-b:
Post-fit $ \mathcal{D}_\mathrm{VBF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. A uniform binning is applied for visualization, with the true binning range indicated on the x-axis. The binning scheme optimized for the 2018 data set is used. |
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Figure 4-c:
Post-fit $ \mathcal{D}_\mathrm{VBF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. A uniform binning is applied for visualization, with the true binning range indicated on the x-axis. The binning scheme optimized for the 2018 data set is used. |
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Figure 4-d:
Post-fit $ \mathcal{D}_\mathrm{VBF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. A uniform binning is applied for visualization, with the true binning range indicated on the x-axis. The binning scheme optimized for the 2018 data set is used. |
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Figure 5:
Post-fit $ \mathcal{D}_\mathrm{VBF,ggF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. The binning scheme optimized for the 2018 data set is used. |
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Figure 5-a:
Post-fit $ \mathcal{D}_\mathrm{VBF,ggF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. The binning scheme optimized for the 2018 data set is used. |
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Figure 5-b:
Post-fit $ \mathcal{D}_\mathrm{VBF,ggF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. The binning scheme optimized for the 2018 data set is used. |
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Figure 5-c:
Post-fit $ \mathcal{D}_\mathrm{VBF,ggF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. The binning scheme optimized for the 2018 data set is used. |
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Figure 5-d:
Post-fit $ \mathcal{D}_\mathrm{VBF,ggF}\ $ distributions in the $ \Delta\Phi_\mathrm{{jj}}\ $ bins of the SR for the full Run 2 data set. Systematic uncertainties are shown as dashed gray bands. The signal is shown both stacked and superimposed on the background template. The binning scheme optimized for the 2018 data set is used. |
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Figure 6:
Measured fiducial cross section of the VBF and ggF production modes. Coloured markers represent the extracted cross section values from data, with error bars showing the combined statistical and systematic uncertainties. The gray bands indicate the statistical uncertainties. The coloured histogram corresponds to the expected SM prediction, simulated with POWHEG + JHUGen + Pythia generators. The lower panel displays the ratio of the measured values to the SM expectation. |
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Figure 7:
Two dimensional expected and observed scans for the pairs of Wilson coefficients $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (top left), $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (top right), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (bottom left) and $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (bottom right) are presented. Solid (dotted) lines correspond to the 68% CL (95% CL) contours. |
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Figure 7-a:
Two dimensional expected and observed scans for the pairs of Wilson coefficients $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (top left), $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (top right), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (bottom left) and $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (bottom right) are presented. Solid (dotted) lines correspond to the 68% CL (95% CL) contours. |
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Figure 7-b:
Two dimensional expected and observed scans for the pairs of Wilson coefficients $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (top left), $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (top right), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (bottom left) and $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (bottom right) are presented. Solid (dotted) lines correspond to the 68% CL (95% CL) contours. |
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Figure 7-c:
Two dimensional expected and observed scans for the pairs of Wilson coefficients $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (top left), $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (top right), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (bottom left) and $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (bottom right) are presented. Solid (dotted) lines correspond to the 68% CL (95% CL) contours. |
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Figure 7-d:
Two dimensional expected and observed scans for the pairs of Wilson coefficients $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (top left), $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (top right), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (bottom left) and $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (bottom right) are presented. Solid (dotted) lines correspond to the 68% CL (95% CL) contours. |
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Figure 8:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-a:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-b:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-c:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-d:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-e:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 8-f:
Expected and observed scans for the Wilson coefficients $ c_\text{HW} $ (top left), $ c_\text{HWB} $ (middle left), $ c_\text{HB} $ (bottom left), $ c_{\text{H}\tilde{\text{W}}} $ (top right), $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (middle right) and $ c_{\text{H}\tilde{\text{B}}} $ (bottom right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 9:
Expected and observed scans for the Wilson coefficients $ c_\text{HD} $ (left) and $ c_{\text{H}\Box} $ (right) are shown. The results are presented for the scenario where all other coefficients are fixed to their SM values. Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 9-a:
Expected and observed scans for the Wilson coefficients $ c_\text{HD} $ (left) and $ c_{\text{H}\Box} $ (right) are shown. The results are presented for the scenario where all other coefficients are fixed to their SM values. Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 9-b:
Expected and observed scans for the Wilson coefficients $ c_\text{HD} $ (left) and $ c_{\text{H}\Box} $ (right) are shown. The results are presented for the scenario where all other coefficients are fixed to their SM values. Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 10:
Expected and observed scans for the Wilson coefficients $ c_\text{HG} $ (left) and $ c_{\text{H}\tilde{\text{G}}} $ (right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
png pdf |
Figure 10-a:
Expected and observed scans for the Wilson coefficients $ c_\text{HG} $ (left) and $ c_{\text{H}\tilde{\text{G}}} $ (right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
png pdf |
Figure 10-b:
Expected and observed scans for the Wilson coefficients $ c_\text{HG} $ (left) and $ c_{\text{H}\tilde{\text{G}}} $ (right) are shown. The results are presented for two scenarios: one where all other coefficients are fixed to their SM values (grey) and another where the coefficient with opposite CP-parity is allowed to float in the fit (black). Horizontal lines indicate the one-dimensional 68% and 95% CL contours. |
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Figure 11:
Measured fiducial cross section for VBF production as a function of $ \Delta\Phi_\mathrm{{jj}}\ $ (black) compared to various predictions. The cross section predictions include: the SM (red), the ones obtained from the best-fit of Wilson coefficients of $ c_\text{HW} $, $ c_{\text{H}\tilde{\text{W}}} $ (yellow), $ c_\text{HWB} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $ (blue) and $ c_\text{HB} $, $ c_{\text{H}\tilde{\text{B}}} $ (green). The difference between the data and the predictions are displayed in the bottom panel. |
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Figure 12:
Measured fiducial cross section for VBF production as a function of $ \Delta\Phi_\mathrm{{jj}}\ $ (black) compared to various predictions. The cross section predictions include: the SM (red), the ones obtained from the best-fit of Wilson coefficients of $ c_{\text{H}\Box} $ (dark grey) and $ c_\text{HD} $ (light grey). The difference between the data and the predictions are displayed in the bottom panel. |
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Figure 13:
Measured fiducial cross section for ggF production as a function of $ \Delta\Phi_\mathrm{{jj}}\ $ (black) compared to various predictions. The cross section predictions include: the SM (blue) and the ones obtained from the best-fit of Wilson coefficients of $ c_\text{HG} $, $ c_{\text{H}\tilde{\text{G}}} $ (magenta). The difference between the data and the predictions are displayed in the bottom panel. |
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Figure A1:
Measured fiducial cross section of the VBF production mode. Black markers represent the extracted cross section values from data, with error bars showing the combined statistical and systematic uncertainties. The gray bands indicate the statistical uncertainties. The red histogram corresponds to the expected SM prediction, simulated with POWHEG + JHUGen + Pythia generators. The lower panel displays the ratio of the measured values to the SM expectation. |
| Tables | |
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Table 1:
Definition of the analysis phase spaces. |
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Table 2:
Definition of the $ \Delta\Phi_\mathrm{{jj}}\ $ bins. |
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Table 3:
Definition of the fiducial phase space. Observables are defined using generator-level quantities. |
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Table 4:
Set of ADNN input features. |
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Table 5:
Contributions of different sources of uncertainty in the cross section measurement, expressed as a percentage of the total uncertainty ($ \Delta \sigma_i / \Delta \sigma_{\text{tot}} \times $ 100). For asymmetric errors, the largest of the up and down uncertainties is reported. The systematic component includes all sources except for background normalization, which is part of the statistical component. |
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Table 6:
Measured fiducial cross section summing VBF and ggF production modes. The total (statistical and systematic) and statistical errors corresponding to the 68% CL are shown. Results are reported with two decimal numbers in order to highlight the difference between the total and the statistical error. The observed significance with respect to the background only hypothesis is computed accounting for the total uncertainty. |
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Table 7:
Measured fiducial cross section of VBF and ggF production modes. The measurement is performed through a simultaneous fit, where the contributions from VBF and ggF production are determined independently in each bin. Results are reported with two decimal numbers in order to highlight the difference between the total and the statistical error. All parameters of interest are constrained to be positive. The observed significance with respect to the background-only hypothesis is computed accounting for the total uncertainty. |
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Table 8:
Measured fiducial cross section of VBF production mode while fixing ggF to SM. The total (statistical and systematic) and statistical errors corresponding to the 68% CL are shown. Results are reported with two decimal numbers in order to highlight the difference between the total and the statistical error. The observed significance with respect to the background only hypothesis is computed accounting for the total uncertainty. |
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Table 9:
List of $ X^{2}H^{2} $ and $ H^{4}D^{2} $ operators and their corresponding Wilson coefficients. |
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Table 10:
Summary of the constraints on Wilson coefficients, including best-fit values, 68% and 95% CL intervals. The observed significance with respect to the SM scenario is shown in the last column. The constraints on $ c_{\text{H}\Box} $ and $ c_\text{HD} $ were obtained from individual fits with all other coefficients fixed to their SM values. For the remaining coefficients, results were obtained from fits where the corresponding CP-even or CP-odd partner was allowed to float, while all other coefficients were fixed to their SM values. |
| Summary |
| This note presents a model-independent measurement of the Higgs boson differential production cross section in its decay to a pair of W bosons, with a final state that includes two jets and different-flavor dilepton $ (e\mu) $. The measurement is based on proton-proton collision data recorded by the CMS detector between 2016 and 2018, corresponding to a total integrated luminosity of 138 fb$^{-1}$ at a center-of-mass energy of 13 TeV. The production cross sections are measured as a function of the azimuthal angle difference between the two jets. Three different signal extraction configurations are employed to measure the overall Higgs boson cross section in association with two jets produced through VBF and ggF modes. No significant deviations from the standard model were found in any of the differential distributions. Differential cross section measurements are further utilized to constrain Wilson coefficients within the standard model effective field theory framework. The strongest constraints were obtained for the VBF cross section measurement under the assumption of the CP-even $ c_{\text{HW}} $ coefficient, as well as for the ggF cross section measurement, which is sensitive to the CP-even $ c_{\text{HG}} $ coefficient. All results were found to be consistent with the standard model expectations. |
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