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| CMS-HIG-24-006 ; CERN-EP-2026-100 | ||
| Constraints on anomalous Higgs boson couplings to vector bosons and fermions using the $ \gamma\gamma $ final state in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 14 May 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: Possible anomalous couplings of the Higgs boson to vector bosons and fermions are studied using Higgs boson candidates decaying to a pair of photons. The study is based on proton-proton collision data at $ \sqrt{s} = $ 13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Events with Higgs boson candidates produced via gluon fusion, electroweak vector boson fusion and in association with a vector boson, are categorized using matrix element techniques and multivariate discriminants. The $ CP $ properties of the Higgs boson couplings to gluons through loops of heavy particles, as well as the tensor structure of its interactions with two electroweak bosons, are investigated. The results are interpreted in terms of the fractional contributions of anomalous Higgs boson couplings to the total production cross section of each process and are found to be consistent with the standard model expectations. | ||
| Links: e-print arXiv:2605.14245 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
LO SM Feynman diagrams for the (a) $ \mathrm{g}\mathrm{g}\mathrm{H} $, (b) $ \mathrm{VBF} $, and (c) VH production processes, as well as for the (d) $ \mathrm{H}\to\gamma\gamma $ decay mode. |
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Figure 1-a:
LO SM Feynman diagrams for the (a) $ \mathrm{g}\mathrm{g}\mathrm{H} $, (b) $ \mathrm{VBF} $, and (c) VH production processes, as well as for the (d) $ \mathrm{H}\to\gamma\gamma $ decay mode. |
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Figure 1-b:
LO SM Feynman diagrams for the (a) $ \mathrm{g}\mathrm{g}\mathrm{H} $, (b) $ \mathrm{VBF} $, and (c) VH production processes, as well as for the (d) $ \mathrm{H}\to\gamma\gamma $ decay mode. |
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Figure 1-c:
LO SM Feynman diagrams for the (a) $ \mathrm{g}\mathrm{g}\mathrm{H} $, (b) $ \mathrm{VBF} $, and (c) VH production processes, as well as for the (d) $ \mathrm{H}\to\gamma\gamma $ decay mode. |
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Figure 1-d:
LO SM Feynman diagrams for the (a) $ \mathrm{g}\mathrm{g}\mathrm{H} $, (b) $ \mathrm{VBF} $, and (c) VH production processes, as well as for the (d) $ \mathrm{H}\to\gamma\gamma $ decay mode. |
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Figure 2:
Leading-order SM Feynman diagrams for the process in which a Higgs boson decaying into a pair of photons is produced via gluon fusion in association with two jets (left) and via vector boson fusion (right). |
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Figure 2-a:
Leading-order SM Feynman diagrams for the process in which a Higgs boson decaying into a pair of photons is produced via gluon fusion in association with two jets (left) and via vector boson fusion (right). |
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Figure 2-b:
Leading-order SM Feynman diagrams for the process in which a Higgs boson decaying into a pair of photons is produced via gluon fusion in association with two jets (left) and via vector boson fusion (right). |
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Figure 3:
Topologies of the H production and decay, useful for the measurement of $ \mathrm{H}\mathrm{V}\mathrm{V} $ couplings: EW vector boson fusion $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1\mathrm{V}_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \mathrm{H} + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \gamma_1\gamma_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} $ (left) and associated production $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1 \to \mathrm{V}_2\mathrm{H} \to \gamma_1\gamma_2 (\mathrm{ff}) $ (right). The figure on the left is valid also to describe gluon fusion events in association with two jets, useful for the measurement of $ \mathrm{H}\mathrm{g}\mathrm{g} $ couplings, when $ \mathrm{V} = \mathrm{g} $. The incoming partons are shown in brown and the intermediate or final-state particles are shown in green and red. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [42,47,50]. |
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Figure 3-a:
Topologies of the H production and decay, useful for the measurement of $ \mathrm{H}\mathrm{V}\mathrm{V} $ couplings: EW vector boson fusion $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1\mathrm{V}_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \mathrm{H} + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \gamma_1\gamma_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} $ (left) and associated production $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1 \to \mathrm{V}_2\mathrm{H} \to \gamma_1\gamma_2 (\mathrm{ff}) $ (right). The figure on the left is valid also to describe gluon fusion events in association with two jets, useful for the measurement of $ \mathrm{H}\mathrm{g}\mathrm{g} $ couplings, when $ \mathrm{V} = \mathrm{g} $. The incoming partons are shown in brown and the intermediate or final-state particles are shown in green and red. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [42,47,50]. |
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Figure 3-b:
Topologies of the H production and decay, useful for the measurement of $ \mathrm{H}\mathrm{V}\mathrm{V} $ couplings: EW vector boson fusion $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1\mathrm{V}_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \mathrm{H} + \mathrm{q}_1^{'}\mathrm{q}_2^{'} \to \gamma_1\gamma_2 + \mathrm{q}_1^{'}\mathrm{q}_2^{'} $ (left) and associated production $ \mathrm{q}_1 \mathrm{q}_2\to \mathrm{V}_1 \to \mathrm{V}_2\mathrm{H} \to \gamma_1\gamma_2 (\mathrm{ff}) $ (right). The figure on the left is valid also to describe gluon fusion events in association with two jets, useful for the measurement of $ \mathrm{H}\mathrm{g}\mathrm{g} $ couplings, when $ \mathrm{V} = \mathrm{g} $. The incoming partons are shown in brown and the intermediate or final-state particles are shown in green and red. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [42,47,50]. |
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Figure 4:
Distribution of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) discriminant for the SM $ \mathrm{VBF} $ signal and for four anomalous coupling hypotheses, shown together with the main resonant background (SM $ \mathrm{g}\mathrm{g}\mathrm{H} $ production), and the continuum diphoton background. The distributions are shown after the $ \mathrm{VBF} $ preselection described in the text and are normalized to the unit area. The vertical dashed lines indicate the category boundaries applied in the analysis. |
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Figure 4-a:
Distribution of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) discriminant for the SM $ \mathrm{VBF} $ signal and for four anomalous coupling hypotheses, shown together with the main resonant background (SM $ \mathrm{g}\mathrm{g}\mathrm{H} $ production), and the continuum diphoton background. The distributions are shown after the $ \mathrm{VBF} $ preselection described in the text and are normalized to the unit area. The vertical dashed lines indicate the category boundaries applied in the analysis. |
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Figure 4-b:
Distribution of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) discriminant for the SM $ \mathrm{VBF} $ signal and for four anomalous coupling hypotheses, shown together with the main resonant background (SM $ \mathrm{g}\mathrm{g}\mathrm{H} $ production), and the continuum diphoton background. The distributions are shown after the $ \mathrm{VBF} $ preselection described in the text and are normalized to the unit area. The vertical dashed lines indicate the category boundaries applied in the analysis. |
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Figure 5:
Distributions of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) outputs for simulation (blue filled histograms, normalized to the data integral) and Drell-Yan data events (black markers). The corresponding ratio plots are shown in the bottom panels. The systematic uncertainty is estimated by comparing NLO and LO Drell-Yan simulations, and is treated as a shape uncertainty. |
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Figure 5-a:
Distributions of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) outputs for simulation (blue filled histograms, normalized to the data integral) and Drell-Yan data events (black markers). The corresponding ratio plots are shown in the bottom panels. The systematic uncertainty is estimated by comparing NLO and LO Drell-Yan simulations, and is treated as a shape uncertainty. |
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Figure 5-b:
Distributions of the $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $ (left) and $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ (right) outputs for simulation (blue filled histograms, normalized to the data integral) and Drell-Yan data events (black markers). The corresponding ratio plots are shown in the bottom panels. The systematic uncertainty is estimated by comparing NLO and LO Drell-Yan simulations, and is treated as a shape uncertainty. |
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Figure 6:
Output scores for the VH leptonic BDTs, $ \mathcal{D}^\mathrm{\mathrm{W}\mathrm{H} lep}_\mathrm{BSM} $ (upper left), $ \mathcal{D}^\mathrm{\mathrm{Z}\mathrm{H} lep}_\mathrm{BSM} $ (upper right), $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ (lower) trained to separate the SM H signal from $ CP $-odd $ (f_{a_3}=1) $ sample. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the gray/blue bars. The simulated signal and background distributions are normalized to the luminosity of the data. To increase its visibility, after the normalization, the signal is scaled by a factor of either 300 or 500 for the different discriminants. For the $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ distribution, a requirement of $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{STXS} > $ 0.619 is applied to exclude events not used in the analysis. A systematic uncertainty is assigned to the component of the nonresonant background determined from a fit to data, to account for discrepancies between data and simulation. |
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Figure 6-a:
Output scores for the VH leptonic BDTs, $ \mathcal{D}^\mathrm{\mathrm{W}\mathrm{H} lep}_\mathrm{BSM} $ (upper left), $ \mathcal{D}^\mathrm{\mathrm{Z}\mathrm{H} lep}_\mathrm{BSM} $ (upper right), $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ (lower) trained to separate the SM H signal from $ CP $-odd $ (f_{a_3}=1) $ sample. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the gray/blue bars. The simulated signal and background distributions are normalized to the luminosity of the data. To increase its visibility, after the normalization, the signal is scaled by a factor of either 300 or 500 for the different discriminants. For the $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ distribution, a requirement of $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{STXS} > $ 0.619 is applied to exclude events not used in the analysis. A systematic uncertainty is assigned to the component of the nonresonant background determined from a fit to data, to account for discrepancies between data and simulation. |
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Figure 6-b:
Output scores for the VH leptonic BDTs, $ \mathcal{D}^\mathrm{\mathrm{W}\mathrm{H} lep}_\mathrm{BSM} $ (upper left), $ \mathcal{D}^\mathrm{\mathrm{Z}\mathrm{H} lep}_\mathrm{BSM} $ (upper right), $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ (lower) trained to separate the SM H signal from $ CP $-odd $ (f_{a_3}=1) $ sample. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the gray/blue bars. The simulated signal and background distributions are normalized to the luminosity of the data. To increase its visibility, after the normalization, the signal is scaled by a factor of either 300 or 500 for the different discriminants. For the $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ distribution, a requirement of $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{STXS} > $ 0.619 is applied to exclude events not used in the analysis. A systematic uncertainty is assigned to the component of the nonresonant background determined from a fit to data, to account for discrepancies between data and simulation. |
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Figure 6-c:
Output scores for the VH leptonic BDTs, $ \mathcal{D}^\mathrm{\mathrm{W}\mathrm{H} lep}_\mathrm{BSM} $ (upper left), $ \mathcal{D}^\mathrm{\mathrm{Z}\mathrm{H} lep}_\mathrm{BSM} $ (upper right), $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ (lower) trained to separate the SM H signal from $ CP $-odd $ (f_{a_3}=1) $ sample. The statistical uncertainty in the data points is denoted as vertical bars and that on the background simulation by the gray/blue bars. The simulated signal and background distributions are normalized to the luminosity of the data. To increase its visibility, after the normalization, the signal is scaled by a factor of either 300 or 500 for the different discriminants. For the $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{BSM} $ distribution, a requirement of $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} MET}_\mathrm{STXS} > $ 0.619 is applied to exclude events not used in the analysis. A systematic uncertainty is assigned to the component of the nonresonant background determined from a fit to data, to account for discrepancies between data and simulation. |
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Figure 7:
Signal and background distributions for the MELA discriminants $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (right) used in the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis. Events are required to have two jets with $ p_{\mathrm{T}} > $ 30 GeV. The nonresonant background is normalized to the data. The dashed vertical lines indicate the bin boundaries applied in the analysis. A 10% systematic uncertainty is assigned to the component of the nonresonant background, obtained from a fit to data, to account for discrepancies between data and simulation. |
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Figure 7-a:
Signal and background distributions for the MELA discriminants $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (right) used in the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis. Events are required to have two jets with $ p_{\mathrm{T}} > $ 30 GeV. The nonresonant background is normalized to the data. The dashed vertical lines indicate the bin boundaries applied in the analysis. A 10% systematic uncertainty is assigned to the component of the nonresonant background, obtained from a fit to data, to account for discrepancies between data and simulation. |
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Figure 7-b:
Signal and background distributions for the MELA discriminants $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (right) used in the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis. Events are required to have two jets with $ p_{\mathrm{T}} > $ 30 GeV. The nonresonant background is normalized to the data. The dashed vertical lines indicate the bin boundaries applied in the analysis. A 10% systematic uncertainty is assigned to the component of the nonresonant background, obtained from a fit to data, to account for discrepancies between data and simulation. |
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Figure 8:
Definition of the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis categories defined in bins of $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ and $ \mathcal{D}^\mathrm{\mathrm{g}\mathrm{g}\mathrm{H}}_\mathrm{STXS} $ for negative (left) and positive (right) values of $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $. |
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Figure 8-a:
Definition of the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis categories defined in bins of $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ and $ \mathcal{D}^\mathrm{\mathrm{g}\mathrm{g}\mathrm{H}}_\mathrm{STXS} $ for negative (left) and positive (right) values of $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $. |
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Figure 8-b:
Definition of the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis categories defined in bins of $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ and $ \mathcal{D}^\mathrm{\mathrm{g}\mathrm{g}\mathrm{H}}_\mathrm{STXS} $ for negative (left) and positive (right) values of $ \mathcal{D}_{CP}^{\mathrm{g}\mathrm{g}\mathrm{H}} $. |
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Figure 9:
Examples of fits to the $ m_{\gamma\gamma} $ distribution for SM signal samples with $ m_\mathrm{H} = $ 125 GeV are shown for the luminosity-weighted average of the four data-taking periods, in two categories targeting $ \mathrm{VBF} $ process, one dominated by SM-like (left) events and the other by BSM-like (right) events. Different Higgs boson production processes are summed according to their expected SM cross sections. The points represent simulation events weighted by their respective event weights. Colored lines represent the individual signal models for each data-taking year. The effective mass resolution ($ \sigma_{\text{eff}} $) of the $ m_{\gamma\gamma} $ distribution is also indicated in the figure. |
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Figure 9-a:
Examples of fits to the $ m_{\gamma\gamma} $ distribution for SM signal samples with $ m_\mathrm{H} = $ 125 GeV are shown for the luminosity-weighted average of the four data-taking periods, in two categories targeting $ \mathrm{VBF} $ process, one dominated by SM-like (left) events and the other by BSM-like (right) events. Different Higgs boson production processes are summed according to their expected SM cross sections. The points represent simulation events weighted by their respective event weights. Colored lines represent the individual signal models for each data-taking year. The effective mass resolution ($ \sigma_{\text{eff}} $) of the $ m_{\gamma\gamma} $ distribution is also indicated in the figure. |
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Figure 9-b:
Examples of fits to the $ m_{\gamma\gamma} $ distribution for SM signal samples with $ m_\mathrm{H} = $ 125 GeV are shown for the luminosity-weighted average of the four data-taking periods, in two categories targeting $ \mathrm{VBF} $ process, one dominated by SM-like (left) events and the other by BSM-like (right) events. Different Higgs boson production processes are summed according to their expected SM cross sections. The points represent simulation events weighted by their respective event weights. Colored lines represent the individual signal models for each data-taking year. The effective mass resolution ($ \sigma_{\text{eff}} $) of the $ m_{\gamma\gamma} $ distribution is also indicated in the figure. |
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Figure 10:
Likelihood scan for the expected and observed constraints of the $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous couplings parameters. |
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Figure 10-a:
Likelihood scan for the expected and observed constraints of the $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous couplings parameters. |
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Figure 10-b:
Likelihood scan for the expected and observed constraints of the $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous couplings parameters. |
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Figure 10-c:
Likelihood scan for the expected and observed constraints of the $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous couplings parameters. |
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Figure 10-d:
Likelihood scan for the expected and observed constraints of the $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous couplings parameters. |
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Figure 11:
Invariant mass distributions are presented separately for categories optimized for $ \mathrm{VBF} $ process (upper left), hadronic VH (upper right), and leptonic VH (lower left). The best fit signal-plus-background model is shown overlaid on the S/(S+B)-weighted distribution of the data points (black) from the fit to the $ f_{a3} $ anomalous coupling parameter. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The lower right plot shows the combined distribution across all categories. Here, S and B represent the expected number of signal and background events in the mass peak region. The green and yellow bands correspond to the one and two standard deviation uncertainties on the background component of the fit. The solid red line indicates the total signal-plus-background prediction, while the dashed red line represents the background-only contribution. The lower panel in each plot displays the residuals obtained by subtracting the background component from the data. |
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Figure 11-a:
Invariant mass distributions are presented separately for categories optimized for $ \mathrm{VBF} $ process (upper left), hadronic VH (upper right), and leptonic VH (lower left). The best fit signal-plus-background model is shown overlaid on the S/(S+B)-weighted distribution of the data points (black) from the fit to the $ f_{a3} $ anomalous coupling parameter. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The lower right plot shows the combined distribution across all categories. Here, S and B represent the expected number of signal and background events in the mass peak region. The green and yellow bands correspond to the one and two standard deviation uncertainties on the background component of the fit. The solid red line indicates the total signal-plus-background prediction, while the dashed red line represents the background-only contribution. The lower panel in each plot displays the residuals obtained by subtracting the background component from the data. |
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Figure 11-b:
Invariant mass distributions are presented separately for categories optimized for $ \mathrm{VBF} $ process (upper left), hadronic VH (upper right), and leptonic VH (lower left). The best fit signal-plus-background model is shown overlaid on the S/(S+B)-weighted distribution of the data points (black) from the fit to the $ f_{a3} $ anomalous coupling parameter. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The lower right plot shows the combined distribution across all categories. Here, S and B represent the expected number of signal and background events in the mass peak region. The green and yellow bands correspond to the one and two standard deviation uncertainties on the background component of the fit. The solid red line indicates the total signal-plus-background prediction, while the dashed red line represents the background-only contribution. The lower panel in each plot displays the residuals obtained by subtracting the background component from the data. |
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Figure 11-c:
Invariant mass distributions are presented separately for categories optimized for $ \mathrm{VBF} $ process (upper left), hadronic VH (upper right), and leptonic VH (lower left). The best fit signal-plus-background model is shown overlaid on the S/(S+B)-weighted distribution of the data points (black) from the fit to the $ f_{a3} $ anomalous coupling parameter. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The lower right plot shows the combined distribution across all categories. Here, S and B represent the expected number of signal and background events in the mass peak region. The green and yellow bands correspond to the one and two standard deviation uncertainties on the background component of the fit. The solid red line indicates the total signal-plus-background prediction, while the dashed red line represents the background-only contribution. The lower panel in each plot displays the residuals obtained by subtracting the background component from the data. |
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Figure 11-d:
Invariant mass distributions are presented separately for categories optimized for $ \mathrm{VBF} $ process (upper left), hadronic VH (upper right), and leptonic VH (lower left). The best fit signal-plus-background model is shown overlaid on the S/(S+B)-weighted distribution of the data points (black) from the fit to the $ f_{a3} $ anomalous coupling parameter. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The lower right plot shows the combined distribution across all categories. Here, S and B represent the expected number of signal and background events in the mass peak region. The green and yellow bands correspond to the one and two standard deviation uncertainties on the background component of the fit. The solid red line indicates the total signal-plus-background prediction, while the dashed red line represents the background-only contribution. The lower panel in each plot displays the residuals obtained by subtracting the background component from the data. |
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Figure 12:
Distribution of events weighted by S/(S+B), using bins optimized for the $ \mathrm{VBF} $ process. Here, S denotes the sum of all resonant signal events and B represents the nonresonant background. The plot shows the event yields in each bin within the mass window $ m_\mathrm{H} - \sigma_{eff} < m_{\gamma\gamma} < m_\mathrm{H} + \sigma_{eff} $, for both the full BSM hypothesis (orange) and the SM hypothesis (blue). The data points (black dots with error bars) indicate the observed events in the same mass window, after background subtraction, and include statistical uncertainties. |
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Figure 13:
Data points (black) and signal-plus-background model fit for the sum of all the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis categories weighted by S/(S+B), where S is the number of signal events in the mass peak and B is the nonresonant background. The vector $ \vec{\alpha} $ denotes the set of parameters allowed to float in the fit. The one standard deviation (green) and two standard deviation (yellow) bands show the uncertainties in the background component of the fit. The solid red line shows the total signal-plus-background contribution, whereas the dashed red line represents the background component only. The lower panel shows the residuals after subtraction of the background component. |
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Figure 14:
Likelihood profile for the expected and observed constraints on $ CP $-odd anomalous coupling parameters: $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $ (right). |
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Figure 14-a:
Likelihood profile for the expected and observed constraints on $ CP $-odd anomalous coupling parameters: $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $ (right). |
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Figure 14-b:
Likelihood profile for the expected and observed constraints on $ CP $-odd anomalous coupling parameters: $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ (left) and $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $ (right). |
| Tables | |
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Table 1:
List of the $ \mathrm{H}\to\gamma\gamma $ preselection requirements. The EB is the ECAL barrel region, with $ |\eta| < $ 1.442, while EE is the ECAL endcap region, with 1.566 $ < |\eta| < $ 2.5. |
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Table 2:
List of discriminants for separating anomalous couplings from the SM contribution in the $ \mathrm{H}\mathrm{V}\mathrm{V} $ analysis. The third column indicates the targeted discrimination for that specific observable. Discriminants in this table are only used for event categorization. |
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Table 3:
List of discriminants for separating anomalous couplings from the SM contribution in the $ \mathrm{H}\mathrm{g}\mathrm{g} $ analysis. The third column indicates the targeted discrimination for that specific observable. For the $ \mathcal{D}_{0-}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ discriminant, the ``$ \mathrm{g}\mathrm{g}\mathrm{H} $" label indicates that this observable is constructed using matrix elements computed for the $ \mathrm{g}\mathrm{g}\mathrm{H} $ production process to differentiate it from the equivalent discriminant for the $ \mathrm{VBF} $ process ($ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $). Discriminants in this table are only used for event categorization. |
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Table 4:
Definition of the $ \mathrm{VBF} $ categories based on the values of the discriminants $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNbkg} $, $ \mathcal{D}^\mathrm{VBF}_\mathrm{0-} $ and $ \mathcal{D}^\mathrm{VBF}_\mathrm{NNBSM} $. |
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Table 5:
The expected number of signal events in the case of SM H with $ m_\mathrm{H}= $ 125 GeV in analysis categories targeting $ \mathrm{VBF} $ production (qqH). The fraction of the total number of events arising from the $ \mathrm{VBF} $ production process in each analysis category is provided. Entries with values less than 0.1% are not shown. The $ \sigma_{\text{eff}} $, defined as half of the smallest interval containing 68.3% of the $ m_{\gamma\gamma} $ distribution, is listed for each analysis category. The final column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm1\sigma_{\text{eff}} $ window centered on $ m_\mathrm{H} $. |
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Table 6:
Definition of the $ {\mathrm{V}} (\mathrm{q}\mathrm{q})\mathrm{H} $ categories, i.e.,, VH events where the vector boson decays hadronically, based on the values of the discriminants $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} had}_\mathrm{NNbkg} $ and $ \mathcal{D}^\mathrm{\mathrm{V}\mathrm{H} had}_\mathrm{NNBSM} $. |
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Table 7:
The expected number of signal events in the case of SM H with $ m_\mathrm{H}= $ 125 GeV in analysis categories targeting VH associated production in which the vector boson decays hadronically, shown for an integrated luminosity of 138 fb$ ^{-1} $. The fraction of the total number of events arising from the VH production process in each analysis category is provided. Entries with values less than 0.1% are not shown. The $ \sigma_{\text{eff}} $, defined as half of the smallest interval containing 68.3% of the $ m_{\gamma\gamma} $ distribution, is listed for each analysis category. The last column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm1\sigma_{\text{eff}} $ window centered on $ m_\mathrm{H} $. |
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Table 8:
Definition of the $ {\mathrm{V}} (\mathrm{lep})\mathrm{H} $ categories based on the values of the discriminants $ \mathcal{D}_\mathrm{STXS} $ and $ \mathcal{D}_\mathrm{BSM} $. |
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Table 9:
The expected number of signal events in the case of SM H with $ m_\mathrm{H}= $ 125 GeV in analysis categories targeting VH associated production in which the vector boson decays leptonically, shown for an integrated luminosity of 138 fb$ ^{-1} $. The fraction of the total number of events arising from the VH production process in each analysis category is provided. Entries with values less than 0.1% are not shown. The $ \sigma_{\text{eff}} $, defined as half of the smallest interval containing 68.3% of the $ m_{\gamma\gamma} $ distribution, is listed for each analysis category. The last column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm1\sigma_{\text{eff}} $ window centered on $ m_\mathrm{H} $. |
png pdf |
Table 10:
The expected number of signal events in the case of SM H with $ m_\mathrm{H}= $ 125 GeV in analysis categories targeting $ \mathrm{g}\mathrm{g}\mathrm{H} $ production associated with two jets, shown for an integrated luminosity of 138 fb$ ^{-1} $. The fraction of the total number of events arising from the $ \mathrm{g}\mathrm{g}\mathrm{H} $ production process in each analysis category is provided. Entries with values less than 0.1% are not shown. The $ \sigma_{\text{eff}} $, defined as half of the smallest interval containing 68.3% of the $ m_{\gamma\gamma} $ distribution, is listed for each analysis category. The last column shows the expected ratio of signal to signal-plus-background, S/(S+B), where S and B are the numbers of expected signal and background events in a $ \pm1\sigma_{\text{eff}} $ window centered on $ m_\mathrm{H} $. |
png pdf |
Table 11:
Summary of expected and observed results in terms of the best fit value and the 68% CL intervals. |
png pdf |
Table 12:
Summary of expected and observed $ \mathrm{H}\mathrm{V}\mathrm{V} $ anomalous coupling parameter results in terms of the 95 % CL intervals for the $ \mathrm{H}\mathrm{V}\mathrm{V} $ analysis described in this paper and, for comparison, from the combination of $ \mathrm{H}\to4\ell $ + $ \mathrm{H}\to\tau\tau $ channels in Ref. [none-none-none]. |
png pdf |
Table 13:
Summary of results in terms of the best fit values for the $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ and $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $ parameters with the best fit values and allowed 68% CL and 95% CL intervals. The $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ constraints obtained in this work (shown in bold) are compared to those obtained in the $ \mathrm{t}\mathrm{H} $ and $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} \mathrm{H}\to\gamma\gamma $ [20], $ \mathrm{g}\mathrm{g}\mathrm{H} \mathrm{H}\to4\ell $ [none-none-none-none], $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ [35] and $ \mathrm{H}\to\tau\tau $ [none-none-none] channels, respectively. The most stringent constraint on $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ has been obtained in [none-none-none] from the combination of the $ \mathrm{H}\to\tau\tau $ and $ \mathrm{H}\to4\ell $ [none-none-none-none] decay channels. The interpretation of the $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $ result under the assumption of the top quark dominance in the gluon fusion loop is presented in terms of $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $. The most stringent constraint on $ f_{CP}^{\mathrm{H}\mathrm{t}\mathrm{t}} $ comes from [none-none-none], where the $ \mathrm{g}\mathrm{g}\mathrm{H} $, $ \mathrm{t}\mathrm{H} $ and $ \mathrm{t}\overline{\mathrm{t}}\mathrm{H} $ measurements are combined in the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to4\ell $ [none-none-none-none], and $ \mathrm{H}\to\gamma\gamma $ [20] decay channels. |
| Summary |
| A search for possible anomalous interactions between the Higgs boson (H) and vector bosons and gluons, including potential $ CP $-violating effects, has been presented. The search is based on proton--proton collision data at $ \sqrt{s} = $ 13 TeV collected by the CMS experiment corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The analysis targets the Higgs boson candidates reconstructed in the diphoton decay channel in events produced via vector boson fusion and associated production with a vector boson. For the first time, anomalous couplings between the Higgs boson and vector boson are studied in this decay channel. The observed limits provide the most stringent constraints on some of the targeted effective cross-section fractions among the CMS results published to date. This analysis also investigates anomalous Higgs boson coupling to gluons in events produced via gluon fusion in association with two jets. The observed constraints on the effective cross section fraction for a $ CP $-odd anomalous H-gluon coupling are comparable to the best CMS constraints obtained so far in other decay channels. Since systematic uncertainties largely cancel in the considered cross-section fractions, all measurements are currently limited by statistical precision. |
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