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| CMS-HIG-23-016 ; CERN-EP-2024-294 | ||
| Constraints on standard model effective field theory for a Higgs boson produced in association with W or Z bosons in the H $ \to \mathrm{b}\overline{\mathrm{b}} $ decay channel in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 25 November 2024 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: A standard model effective field theory (SMEFT) analysis with dimension-six operators probing nonresonant new physics effects is performed in the Higgs-strahlung process, where the Higgs boson is produced in association with a W or Z boson, in proton-proton collisions at a center-of-mass energy of 13 TeV. The final states in which the W or Z boson decays leptonically and the Higgs boson decays to a pair of bottom quarks are considered. The analyzed data were collected by the CMS experiment between 2016 and 2018 and correspond to an integrated luminosity of 138 fb$ ^{-1} $. An approach designed to simultaneously optimize the sensitivity to Wilson coefficients of multiple SMEFT operators is employed. Likelihood scans as functions of the Wilson coefficients that carry SMEFT sensitivity in this final state are performed for different expansions in SMEFT. The results are consistent with the predictions of the standard model. | ||
| Links: e-print arXiv:2411.16907 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative Feynman diagrams for VH production sensitive to different dimension-six operators. The EFT effects contribute in vertices highlighted with a black dot. The diagram on the left shows effects due to $ {\cal O}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}_{\mathrm{H}\mathrm{u}} $, and $ {\cal O}_{\mathrm{H}\mathrm{d}} $. The diagram at the center also includes contributions due to $ {\cal O}_{\mathrm{H}\textrm{D}} $ and $ {\cal O}_{\mathrm{H}\mathrm{W}\textrm{B}} $. The diagram on the right displays effects from $ \mathcal{O}_{\mathrm{H}\mathrm{W}} $, $ \mathcal{O}_{\mathrm{H}\mathrm{W}\textrm{B}} $, $ \mathcal{O}_{\mathrm{H}\textrm{B}} $, and their CP conjugates. |
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Figure 1-a:
Representative Feynman diagrams for VH production sensitive to different dimension-six operators. The EFT effects contribute in vertices highlighted with a black dot. The diagram on the left shows effects due to $ {\cal O}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}_{\mathrm{H}\mathrm{u}} $, and $ {\cal O}_{\mathrm{H}\mathrm{d}} $. The diagram at the center also includes contributions due to $ {\cal O}_{\mathrm{H}\textrm{D}} $ and $ {\cal O}_{\mathrm{H}\mathrm{W}\textrm{B}} $. The diagram on the right displays effects from $ \mathcal{O}_{\mathrm{H}\mathrm{W}} $, $ \mathcal{O}_{\mathrm{H}\mathrm{W}\textrm{B}} $, $ \mathcal{O}_{\mathrm{H}\textrm{B}} $, and their CP conjugates. |
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Figure 1-b:
Representative Feynman diagrams for VH production sensitive to different dimension-six operators. The EFT effects contribute in vertices highlighted with a black dot. The diagram on the left shows effects due to $ {\cal O}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}_{\mathrm{H}\mathrm{u}} $, and $ {\cal O}_{\mathrm{H}\mathrm{d}} $. The diagram at the center also includes contributions due to $ {\cal O}_{\mathrm{H}\textrm{D}} $ and $ {\cal O}_{\mathrm{H}\mathrm{W}\textrm{B}} $. The diagram on the right displays effects from $ \mathcal{O}_{\mathrm{H}\mathrm{W}} $, $ \mathcal{O}_{\mathrm{H}\mathrm{W}\textrm{B}} $, $ \mathcal{O}_{\mathrm{H}\textrm{B}} $, and their CP conjugates. |
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Figure 1-c:
Representative Feynman diagrams for VH production sensitive to different dimension-six operators. The EFT effects contribute in vertices highlighted with a black dot. The diagram on the left shows effects due to $ {\cal O}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {\cal O}_{\mathrm{H}\mathrm{u}} $, and $ {\cal O}_{\mathrm{H}\mathrm{d}} $. The diagram at the center also includes contributions due to $ {\cal O}_{\mathrm{H}\textrm{D}} $ and $ {\cal O}_{\mathrm{H}\mathrm{W}\textrm{B}} $. The diagram on the right displays effects from $ \mathcal{O}_{\mathrm{H}\mathrm{W}} $, $ \mathcal{O}_{\mathrm{H}\mathrm{W}\textrm{B}} $, $ \mathcal{O}_{\mathrm{H}\textrm{B}} $, and their CP conjugates. |
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Figure 2:
Decay planes and angles in the $ \mathrm{V}(\to \ell_1 \ell_2){\mathrm{H}}(\to \mathrm{b} \overline{\mathrm{b}}) $ production. The $ \Theta $ angle is defined in the VH rest frame, while $ \theta $ is defined in the V rest frame. Figure modified from Ref. [38]. The coordinate system used in the sketch of the decay plane is independent of the general CMS coordinate system that is used for the analysis. |
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Figure 3:
Selected template shapes after the optimization process described in Section 7.3 in the resolved (left) and boosted (right) categories of the 2-lepton channel. The template shapes of the EFT signal components are shown for arbitrary values of the Wilson coefficients: ($ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {c}_{\mathrm{H}\mathrm{u}} $, $ {c}_{\mathrm{H}\mathrm{d}} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $) = (1, 0.8, 1, 1, 2, 2) and (0.2, $-$0.03, 0.2, 0.2, 1, 1) in the resolved and boosted categories, respectively. The SM VH signal is flat by construction. The background is shown as the grey histogram. |
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Figure 3-a:
Selected template shapes after the optimization process described in Section 7.3 in the resolved (left) and boosted (right) categories of the 2-lepton channel. The template shapes of the EFT signal components are shown for arbitrary values of the Wilson coefficients: ($ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {c}_{\mathrm{H}\mathrm{u}} $, $ {c}_{\mathrm{H}\mathrm{d}} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $) = (1, 0.8, 1, 1, 2, 2) and (0.2, $-$0.03, 0.2, 0.2, 1, 1) in the resolved and boosted categories, respectively. The SM VH signal is flat by construction. The background is shown as the grey histogram. |
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Figure 3-b:
Selected template shapes after the optimization process described in Section 7.3 in the resolved (left) and boosted (right) categories of the 2-lepton channel. The template shapes of the EFT signal components are shown for arbitrary values of the Wilson coefficients: ($ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {c}_{\mathrm{H}\mathrm{u}} $, $ {c}_{\mathrm{H}\mathrm{d}} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $) = (1, 0.8, 1, 1, 2, 2) and (0.2, $-$0.03, 0.2, 0.2, 1, 1) in the resolved and boosted categories, respectively. The SM VH signal is flat by construction. The background is shown as the grey histogram. |
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Figure 4:
The BIT templates obtained using a background-only fit to data in the 2-muon (left) and 2-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 4-a:
The BIT templates obtained using a background-only fit to data in the 2-muon (left) and 2-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 4-b:
The BIT templates obtained using a background-only fit to data in the 2-muon (left) and 2-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 4-c:
The BIT templates obtained using a background-only fit to data in the 2-muon (left) and 2-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 4-d:
The BIT templates obtained using a background-only fit to data in the 2-muon (left) and 2-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 5:
The BIT templates obtained using a background-only fit to data in the 1-muon (left) and 1-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
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Figure 5-a:
The BIT templates obtained using a background-only fit to data in the 1-muon (left) and 1-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 5-b:
The BIT templates obtained using a background-only fit to data in the 1-muon (left) and 1-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 5-c:
The BIT templates obtained using a background-only fit to data in the 1-muon (left) and 1-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 5-d:
The BIT templates obtained using a background-only fit to data in the 1-muon (left) and 1-electron (right) final states in the SR for resolved (upper row) and boosted (lower row) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 6:
The BIT templates obtained using a background-only fit to data in the 0-lepton final state in the SR for resolved (left) and boosted (right) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 6-a:
The BIT templates obtained using a background-only fit to data in the 0-lepton final state in the SR for resolved (left) and boosted (right) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 6-b:
The BIT templates obtained using a background-only fit to data in the 0-lepton final state in the SR for resolved (left) and boosted (right) categories considering the 2017 data set. The SM VH signal has been scaled by 20 and 5 for the resolved and boosted BIT templates in the upper and lower row, respectively, for better visualization. The lower panels show the ratio of the data to the background expectation after the background-only fit to the data. |
png pdf |
Figure 7:
Summary of results in terms of best fit value of the Wilson coefficients and the intervals where the test statistic is below 1 and 4, with up to the linear (upper row) and quadratic (lower row) terms in the SMEFT parameterization. These results are obtained either by allowing all Wilson coefficients to float freely at every point of the scan (profiled fit), or by keeping all other Wilson coefficients to their SM values, i.e.,, 0, except for the one that is being considered in the scan (frozen fit). The multiplication factor applies to the sizes of intervals satisfying $ \textit{q} < $ 1 and $ \textit{q} < $ 4 but not to the values of the CIs on the right-hand side of the figure, which correspond to the profiled constraints in all cases. |
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Figure 7-a:
Summary of results in terms of best fit value of the Wilson coefficients and the intervals where the test statistic is below 1 and 4, with up to the linear (upper row) and quadratic (lower row) terms in the SMEFT parameterization. These results are obtained either by allowing all Wilson coefficients to float freely at every point of the scan (profiled fit), or by keeping all other Wilson coefficients to their SM values, i.e.,, 0, except for the one that is being considered in the scan (frozen fit). The multiplication factor applies to the sizes of intervals satisfying $ \textit{q} < $ 1 and $ \textit{q} < $ 4 but not to the values of the CIs on the right-hand side of the figure, which correspond to the profiled constraints in all cases. |
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Figure 7-b:
Summary of results in terms of best fit value of the Wilson coefficients and the intervals where the test statistic is below 1 and 4, with up to the linear (upper row) and quadratic (lower row) terms in the SMEFT parameterization. These results are obtained either by allowing all Wilson coefficients to float freely at every point of the scan (profiled fit), or by keeping all other Wilson coefficients to their SM values, i.e.,, 0, except for the one that is being considered in the scan (frozen fit). The multiplication factor applies to the sizes of intervals satisfying $ \textit{q} < $ 1 and $ \textit{q} < $ 4 but not to the values of the CIs on the right-hand side of the figure, which correspond to the profiled constraints in all cases. |
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Figure 8:
Profiled limits on the energy scale $ \Lambda $ for three different assumptions for each Wilson coefficient while fixing the other Wilson coefficients to their SM values with up to the linear (upper row) and quadratic (lower row) terms in SMEFT parameterization. The upper limits on the Wilson coefficients corresponding to $ \textit{q}= $ 4 is used for translating the constraints to $ \Lambda $. |
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Figure 8-a:
Profiled limits on the energy scale $ \Lambda $ for three different assumptions for each Wilson coefficient while fixing the other Wilson coefficients to their SM values with up to the linear (upper row) and quadratic (lower row) terms in SMEFT parameterization. The upper limits on the Wilson coefficients corresponding to $ \textit{q}= $ 4 is used for translating the constraints to $ \Lambda $. |
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Figure 8-b:
Profiled limits on the energy scale $ \Lambda $ for three different assumptions for each Wilson coefficient while fixing the other Wilson coefficients to their SM values with up to the linear (upper row) and quadratic (lower row) terms in SMEFT parameterization. The upper limits on the Wilson coefficients corresponding to $ \textit{q}= $ 4 is used for translating the constraints to $ \Lambda $. |
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Figure 9:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-a:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-b:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-c:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-d:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-e:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 9-f:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ (upper row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (middle row), $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 10:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 10-a:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 10-b:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 10-c:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 10-d:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 10-e:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 10-f:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{u}} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {c}_{\mathrm{H}\mathrm{d}} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 11:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-a:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-b:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-c:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-d:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-e:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 11-f:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
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Figure 12:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-a:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-b:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-c:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-d:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-e:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 12-f:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (upper row), $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {c}_{\mathrm{H}\mathrm{u}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-a:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-b:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-c:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-d:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-e:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
png pdf |
Figure 13-f:
Observed two-dimensional likelihood scans for different pairs of Wilson coefficients: $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ (upper row), $ {c}_{\mathrm{H}\mathrm{d}} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (middle row), $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $ vs. $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $ (lower row) while allowing the other coefficients to float freely at each point of the scan (left) or fixed at their SM values (right) after combining results from all data-taking years and final states. |
| Tables | |
png pdf |
Table 1:
The dimension-six operators in the Warsaw basis affecting VH production at leading order. Here $ {{\mathrm{q}}_{\textrm{L}}} $ refers to a left-handed quark field and is a representation of an SU(2) quark doublets. $ {\mathrm{u}}_{\textrm{R}} $ refers to a right-handed up quark singlet, and $ {\mathrm{d}}_{\textrm{R}} $ a right-handed down quark singlet. |
png pdf |
Table 2:
Selection criteria for the resolved category in the 0-lepton final state. Momenta and masses have units of GeV. |
png pdf |
Table 3:
Selection criteria for the boosted category in the 0-lepton final state. Momenta and masses have units of GeV. |
png pdf |
Table 4:
Selection conditions for the resolved category in the 1-lepton final state. Momenta and masses have units of GeV. |
png pdf |
Table 5:
Selection conditions for the boosted category in the 1-lepton final state. Momenta and masses have units of GeV. |
png pdf |
Table 6:
Selection conditions for the resolved category in the 2-lepton final state. Momenta and masses have units of GeV. |
png pdf |
Table 7:
Selection conditions for the boosted category in the 2-lepton final state. Momenta and masses have units of GeV. |
| Summary |
| A standard model effective field theory (SMEFT) analysis is performed in the Higgs-strahlung process, where the Higgs boson is produced in association with a vector boson (V = W, Z), probing nonresonant new physics effects. Final states with the Higgs boson decaying to a pair of bottom quarks are targeted. Proton-proton collision data collected by the CMS experiment during 2016--2018 at a center-of-mass energy of 13 TeV are used, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Leptonic decay modes of W and Z bosons ($ \mathrm{W}\to\ell\nu $, $ \mathrm{Z}\to\ell\ell $, and $ \mathrm{Z}\to\nu\nu $) are considered, and both resolved- as well as merged-jet topologies are exploited for the $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ decay. A multivariate analysis strategy based on likelihood-free inference methods is adopted for the first time in the CMS experiment to probe the effects of multiple SMEFT operators including those giving rise to CP violation. The strategy employing boosted decision trees makes use of the angular information which is sensitive to the CP structure of SMEFT operators in this final state. Results are consistent with the standard model expectation. Constraints on the Wilson coefficients of six relevant SMEFT operators ($ {c}^{(1)}_{\mathrm{H}\mathrm{q}} $, $ {c}^{(3)}_{\mathrm{H}\mathrm{q}} $, $ {c}_{\mathrm{H}\mathrm{u}} $, $ {c}_{\mathrm{H}\mathrm{d}} $, $ {g}^{\mathrm{Z}\mathrm{Z}}_{2} $, and $ {g}^{\mathrm{Z}\mathrm{Z}}_{4} $) are obtained by performing a simultaneous fit to the data. Constraints on the vector-coupling operators are slightly more stringent than those on the gauge-coupling operators. Lower limits on the energy scales associated with various SMEFT operators are also presented, offering further constraints on different classes of new physics models. Additionally, constraints on two-dimensional planes of Wilson coefficients for all possible pairs are presented to explore correlations between pairs of Wilson coefficients. This constitutes the most comprehensive SMEFT analysis in this channel to date. |
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