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| CMS-PAS-NPS-25-002 | ||
| Search for pair production of additional neutral scalars within the Inert Doublet Model in a final state with two electrons or two muons | ||
| CMS Collaboration | ||
| 2026-03-14 | ||
| Abstract: A search for pair production of new scalars predicted by the Inert Doublet Model is performed using proton-proton collisions collected with the CMS detector at the CERN LHC at $ \sqrt{s}= $13 and 13.6 TeV, corresponding to integrated luminosities of 138 and 35 fb$ ^{-1} $, respectively. Within this model, four additional scalar bosons (H, A, H$ ^{+} $, H$ ^{-} $) are predicted, and because of an additional discrete symmetry, the lightest new scalar, H, is stable, rendering it a viable dark matter candidate. The target final state consists of exactly two opposite-charge same-flavour leptons (electrons or muons), with very little hadronic activity, and missing transverse momentum due to the stable neutral scalars. A parameterised neural network is used to separate the signal from the standard model background. No significant excess of events is observed. Exclusion limits at 95% confidence level are set on the production cross section of the two new neutral scalars, H and A, expressed in terms of their masses, $ m_{\mathrm{H}} $ and $ m_{\mathrm{A}} $, in the $ m_{\mathrm{H}} $ vs. $ m_{\mathrm{A}}-m_\mathrm{H} $ plane. The observed (expected) exclusion region reaches $ m_{\mathrm{H}}=108 (106) $ GeV for $ m_{\mathrm{A}}-m_\mathrm{H}=78 (76) $ GeV and at $ m_{\mathrm{H}}= $ 60 GeV, covers the range of $ m_{\mathrm{A}}-m_\mathrm{H}= $35--90 (32--90) GeV. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ \text{A}\mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \text{H}^{\pm} \mathrm{H}^\mp $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
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Figure 1-a:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ \text{A}\mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \text{H}^{\pm} \mathrm{H}^\mp $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
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Figure 1-b:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ \text{A}\mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \text{H}^{\pm} \mathrm{H}^\mp $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
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Figure 1-c:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ \text{A}\mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \text{H}^{\pm} \mathrm{H}^\mp $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
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Figure 2:
Total signal cross section obtained with MadGraph-5_aMC@NLO in the $ (m_{\text{H}}, m_{\text{A}}-m_{\text{H}}) $ plane for Run 2 (left) and Run 3 (right), computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV with a numerical integration error smaller than 0.1%. The simulated training points (circles) are used for training the classifier and for the final statistical inference. The validation points (crosses) are used for testing the interpolation of the signal. |
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Figure 2-a:
Total signal cross section obtained with MadGraph-5_aMC@NLO in the $ (m_{\text{H}}, m_{\text{A}}-m_{\text{H}}) $ plane for Run 2 (left) and Run 3 (right), computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV with a numerical integration error smaller than 0.1%. The simulated training points (circles) are used for training the classifier and for the final statistical inference. The validation points (crosses) are used for testing the interpolation of the signal. |
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Figure 2-b:
Total signal cross section obtained with MadGraph-5_aMC@NLO in the $ (m_{\text{H}}, m_{\text{A}}-m_{\text{H}}) $ plane for Run 2 (left) and Run 3 (right), computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV with a numerical integration error smaller than 0.1%. The simulated training points (circles) are used for training the classifier and for the final statistical inference. The validation points (crosses) are used for testing the interpolation of the signal. |
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Figure 3:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID) which are calculated using control samples in data, as described in Section 7.4. The combined statistical and experimental uncertainty for the SM prediction is shown as the shaded band. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\text{H}} $,$ m_{\text{A}} $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the statistical uncertainties, while the hashed bands include both statistical and systematic components. |
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Figure 3-a:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID) which are calculated using control samples in data, as described in Section 7.4. The combined statistical and experimental uncertainty for the SM prediction is shown as the shaded band. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\text{H}} $,$ m_{\text{A}} $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the statistical uncertainties, while the hashed bands include both statistical and systematic components. |
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Figure 3-b:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID) which are calculated using control samples in data, as described in Section 7.4. The combined statistical and experimental uncertainty for the SM prediction is shown as the shaded band. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\text{H}} $,$ m_{\text{A}} $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the statistical uncertainties, while the hashed bands include both statistical and systematic components. |
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Figure 3-c:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID) which are calculated using control samples in data, as described in Section 7.4. The combined statistical and experimental uncertainty for the SM prediction is shown as the shaded band. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\text{H}} $,$ m_{\text{A}} $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 3-d:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID) which are calculated using control samples in data, as described in Section 7.4. The combined statistical and experimental uncertainty for the SM prediction is shown as the shaded band. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\text{H}} $,$ m_{\text{A}} $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the statistical uncertainties, while the hashed bands include both statistical and systematic components. |
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Figure 4:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
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Figure 4-a:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 4-b:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 5:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 5-a:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 5-b:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 120 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 6:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 6-a:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 6-b:
Distributions of the pNN output for the data and the SM expectations in the SR after the background-only fit to the data in the (left) $ \mathrm{e}^-\mathrm{e}^+ $ channel and (right) $ \mu^-\mu^+ $ channel for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The combined statistical and experimental uncertainty is shown by the shaded band. The dotted black line represents the signal, referred to as IDM$ (m_{\text{H}},m_{\text{A}}) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 7:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 7-a:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 7-b:
Distributions of the data and the SM expectations in all CRs after the background-only fit to the data for $ m_{\text{H}} = $ 70 and $ m_{\text{A}} = $ 160 GeV. The dilepton $ p_{\mathrm{T}} $ (left plot) is used as the observable in the fit for the two $ \mathrm{W^-}\mathrm{W^+}/{\mathrm{t}\overline{\mathrm{t}}} $ CRs as well as the different-flavour MisID CR, and the pNN output (right plot) is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The combined statistical and experimental uncertainty is shown by the shaded band. The lower panels show the ratio of data to the SM expectation. The error bars show statistical uncertainties, while the hashed bands include both statistical and systematic components. |
png pdf |
Figure 8:
The 95% CL exclusion limits in terms of $ m_{\text{H}} $ and $ m_{\text{A}} - m_{\text{H}} $. The red dashed lines indicate the $ \pm $ 1 standard deviation bands from experimental uncertainties, whilst the black dashed lines indicate the $ \pm $ 1 standard deviation bands from theory uncertainties in the signal samples. The exclusion limits from LEP reinterpretation and relic density constraints are overlaid in green and yellow, respectively [7]. Limits are calculated with the IDM parameters $ m_{\text{H}^{\pm}} = m_{\text{A}} + $ 50 GeV, $ \lambda_2 = $ 1, and $ \lambda_{345} = 10^{-6} $. The limits, however, are insensitive to the choice of the $ \lambda_2 $ value, and to changes in the $ m_{\text{H}^{\pm}} $ and $ \lambda_{345} $ within their allowed values. |
| Tables | |
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Table 1:
Kinematic preselection of dilepton pairs. All events require at least one dilepton pair passing the "Dilepton" quantities, but with no constraints on the charges or flavours. The $ p_{\mathrm{T}} $ of the leading lepton is dictated by the year-specific thresholds of the single-lepton triggers. |
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Table 2:
Signal region selection. Events must also pass the preselection outlined in Table 1. A veto is applied on any event with additional loose leptons. |
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Table 3:
Selections for the control regions. For all events, we require at least one dilepton pair passing the preselection outlined in Table 1, as well as any additional requirements given in this table. The second dilepton in the ZZ CR does not have to pass the selection in Table 1. All regions have a veto on any additional loose leptons. The fit variable refers to the fit procedure described in Section 9. |
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Table 4:
Uncertainty breakdown in the fitted signal strength for two signal mass points. The sources of uncertainty are separated into different groups. |
| Summary |
| The Inert Doublet Model predicts additional scalars, including two neutral scalars H and $ \text{A} $, which couple only to bosons. The lightest neutral scalar, H, is stable and provides a viable dark matter candidate. The pair production of such new scalars is investigated in a final state containing two electrons or two muons. The search is performed using proton-proton collisions at $\sqrt{s}$ 13 (13.6) TeV, delivered by the LHC and recorded by the CMS experiment between 2016 and 2018 (in 2022), with a total integrated luminosity of 138 fb$ ^{-1} $ \ (35 fb$ ^{-1} $ ). After a preselection to remove the largest standard model backgrounds, a parameterised neural network is trained to discriminate the different signal mass points from the remaining backgrounds. Control regions tailored to each of the dominant backgrounds are constructed and used in a simultaneous fit together with the signal region to set 95% confidence level exclusion limits on the signal production cross section in the $ m_{\text{H}} $ vs $ m_{\text{A}}-m_\text{H} $ plane. The observed (expected) exclusion region reaches $ m_{\text{H}}=108 (106) \text{GeV} $ for $ m_{\text{A}}-m_\text{H}=78 (76) \text{GeV} $ and, at $ m_{\text{H}}= $ 60 GeV, covers the range of $ m_{\text{A}}-m_\text{H}= $35--90 (32--90) GeV. These exclusion limits significantly extend the constraints from previous direct and indirect measurements and dark-matter searches. These results represent the first limits on the masses of the neutral scalars in the Inert Doublet Model obtained by a dedicated search using collision data. |
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