Compact Muon Solenoid
LHC, CERN
Visit us: CMS Public Website, CMS Physics ;
Contact us: CMS Publications Committee
| CMS-NPS-25-002 ; CERN-EP-2026-098 | ||
| Search for pair production of additional neutral scalars within the Inert Doublet Model in a final state with two electrons or two muons in proton-proton collisions at $ \sqrt{s} = $ 13 and 13.6 TeV | ||
| CMS Collaboration | ||
| 13 May 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: A first dedicated search for pair production of new scalars predicted by the Inert Doublet Model is performed using proton-proton collisions. Data were collected with the CMS detector at the CERN LHC at $\sqrt{s} = $13 and 13.6 TeV, corresponding to integrated luminosities of 138 fb$ ^{-1} $ and 35 fb$ ^{-1} $, respectively. Within this model, four additional scalar bosons ($\mathrm{H}$, $\mathrm{A}$, $ \mathrm{H}^{+} $, and $ \mathrm{H}^{-} $) are predicted. Through an additional discrete symmetry, the lightest new scalar, H, is stable, rendering it a viable dark matter candidate. These candidates can originate from quark-antiquark annihilation producing an offshell Z boson that decays to a pair of the new scalars. The target final state consists of exactly two opposite-charge same-flavour leptons (electrons or muons), with missing transverse momentum due to the stable neutral scalars, and very little hadronic activity. 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, $\mathrm{H}$ and $\mathrm{A}$, 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) \text{GeV} $ for $ m_{{\mathrm{A}} } -m_{\mathrm{H}}=78 (76) \text{GeV} $ and at $ m_{\mathrm{H}}= $ 70 GeV, covers the range of $ m_{{\mathrm{A}} } -m_{\mathrm{H}}= $ 40--90 (35--90) GeV. | ||
| Links: e-print arXiv:2605.13614 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
png pdf |
Figure 1:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ {\mathrm{A}} \mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \mathrm{\widetilde{H}^{\pm_j}} {\mathrm{H}{\mp}} $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
png pdf |
Figure 1-a:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ {\mathrm{A}} \mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \mathrm{\widetilde{H}^{\pm_j}} {\mathrm{H}{\mp}} $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
png pdf |
Figure 1-b:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ {\mathrm{A}} \mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \mathrm{\widetilde{H}^{\pm_j}} {\mathrm{H}{\mp}} $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
png pdf |
Figure 1-c:
Leading-order Feynman diagrams of: (left) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ production through $ {\mathrm{A}} \mathrm{H} $ production, (middle) $ \mathrm{H}\mathrm{H}\ell^+\ell^-\nu\overline{\nu} $ through $ \mathrm{\widetilde{H}^{\pm_j}} {\mathrm{H}{\mp}} $ production, and (right) $ \mathrm{H}\mathrm{H}\ell^+\ell^- $ through $ \mathrm{h}\mathrm{Z} $ production. |
png pdf |
Figure 2:
Total signal cross section at LO obtained with MadGraph-5\_aMC@NLO in the $ (m_{\mathrm{H}}, m_{{\mathrm{A}} }-m_{\mathrm{H}}) $ plane at (left) $\sqrt{s} = $13 and (right) $\sqrt{s} = $13.6, computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV. 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. |
png pdf |
Figure 2-a:
Total signal cross section at LO obtained with MadGraph-5\_aMC@NLO in the $ (m_{\mathrm{H}}, m_{{\mathrm{A}} }-m_{\mathrm{H}}) $ plane at (left) $\sqrt{s} = $13 and (right) $\sqrt{s} = $13.6, computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV. 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. |
png pdf |
Figure 2-b:
Total signal cross section at LO obtained with MadGraph-5\_aMC@NLO in the $ (m_{\mathrm{H}}, m_{{\mathrm{A}} }-m_{\mathrm{H}}) $ plane at (left) $\sqrt{s} = $13 and (right) $\sqrt{s} = $13.6, computed for leptons with transverse momentum $ p_{\mathrm{T}} > $ 10 GeV. 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. |
png pdf |
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. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\mathrm{H}} $,$ m_{{\mathrm{A}} } $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the data statistical uncertainties, while the hatched bands include both MC statistical and systematic components. |
png pdf |
Figure 3-a:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID), which are calculated using control samples in data, as described in Section 7.4. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\mathrm{H}} $,$ m_{{\mathrm{A}} } $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the data statistical uncertainties, while the hatched bands include both MC statistical and systematic components. |
png pdf |
Figure 3-b:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID), which are calculated using control samples in data, as described in Section 7.4. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\mathrm{H}} $,$ m_{{\mathrm{A}} } $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the data statistical uncertainties, while the hatched bands include both MC statistical and systematic components. |
png pdf |
Figure 3-c:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID), which are calculated using control samples in data, as described in Section 7.4. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\mathrm{H}} $,$ m_{{\mathrm{A}} } $) with the masses given in GeV, and with their normalisation scaled by a factor of 100 for clarity. The first and last bins contain the underflow and overflow events, respectively. The lower panels show the ratio of the data over the SM prediction. The error bars show the data statistical uncertainties, while the hatched bands include both MC statistical and systematic components. |
png pdf |
Figure 3-d:
Distributions of key variables after the preselection and OCSF pair selection for 2016--2018 and 2022 combined. All SM processes are modelled with simulation, except the contribution from events with jets misidentified as leptons (MisID), which are calculated using control samples in data, as described in Section 7.4. Two representative IDM signal samples are also shown, indicated by IDM($ m_{\mathrm{H}} $,$ m_{{\mathrm{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 data statistical uncertainties, while the hatched bands include both MC statistical and systematic components. |
png pdf |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
png pdf |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 120 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. The dotted black line represents the signal, referred to as IDM$ (m_{\mathrm{H}},m_{{\mathrm{A}} }) $, with masses in units of GeV. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
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_{\mathrm{H}} = $ 70 and $ m_{{\mathrm{A}} } = $ 160 GeV. (Left) the dilepton $ p_{\mathrm{T}} $ 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 (right) the pNN output is used for the ZZ CR, both WZ CRs (opposite-charge and same-charge) and the same-charge MisID CRs. The lower panels show the ratio of data to the SM expectation. The error bars show data statistical uncertainties, while the hatched bands include the total uncertainty on the backgrounds. |
png pdf |
Figure 8:
The 95% CL upper limit on $ \sigma_{\mathrm{IDM}} $ as a function of $ m_{{\mathrm{A}} } - m_{\mathrm{H}} $, for $ m_{\mathrm{H}}= $ 70 GeV, separately for the (black circles) Run 2 and (red squares) Run 3 data sets. Limits are calculated with the IDM parameters $ m_{\mathrm{\widetilde{H}^{\pm_j}}} = m_{{\mathrm{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 $ m_{\mathrm{\widetilde{H}^{\pm_j}}} $ and $ \lambda_{345} $ within their allowed values. |
png pdf |
Figure 9:
The 95% CL exclusion limits in terms of $ m_{\mathrm{H}} $ and $ m_{{\mathrm{A}} } - m_{\mathrm{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 theoretical uncertainties in the signal samples. The exclusion limits from the LEP reinterpretation and relic density constraints are overlaid in green and yellow, respectively (see Section 2). Limits are calculated with the IDM parameters $ m_{\mathrm{\widetilde{H}^{\pm_j}}} = m_{{\mathrm{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 $ m_{\mathrm{\widetilde{H}^{\pm_j}}} $ and $ \lambda_{345} $ within their allowed values. |
| Tables | |
png pdf |
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. |
png pdf |
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. |
png pdf |
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. The $ N_\ell $ ($ N_{\ell, {\text{tight}}} $) selection indicates the total number of loose leptons selected and the number of those that must also pass the tight selection criteria. All regions have a veto on any additional loose leptons. The fit variable refers to the fit procedure described in Section 9. |
png pdf |
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 $ {\mathrm{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} = $13 and 13.6 TeV, corresponding to integrated luminosities of 138 fb$ ^{-1} $ and 35 fb$ ^{-1} $, delivered by the LHC and recorded by the CMS experiment between 2016 and 2018, and in 2022, respectively. 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. Dedicated control regions for each of the dominant backgrounds are constructed. A simultaneous fit of the signal region together with the control regions is used to set 95% confidence level exclusion limits on the signal production cross section in the $ m_{\mathrm{H}} $ vs. $ m_{{\mathrm{A}} } -m_{\mathrm{H}} $ plane. The observed (expected) exclusion region reaches $ m_{\mathrm{H}}=108 (106) \text{GeV} $ for $ m_{{\mathrm{A}} } -m_{\mathrm{H}}=78 (76) \text{GeV} $ and, at $ m_{\mathrm{H}}= $ 70 GeV, covers the range of $ m_{{\mathrm{A}} } -m_{\mathrm{H}}= $ 40--90 (35--90) GeV. 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. These exclusion limits significantly extend the constraints from previous direct and indirect measurements and dark-matter searches. |
| References | ||||
| 1 | Particle Data Group Collaboration | Review of particle physics | PRD 110 (2024) 030001 | |
| 2 | L. Roszkowski, E. M. Sessolo, and S. Trojanowski | WIMP dark matter candidates and searches\textemdashcurrent status and future prospects | Rept. Prog. Phys. 81 (2018) 066201 | 1707.06277 |
| 3 | ATLAS Collaboration | Exploration at the high-energy frontier: ATLAS Run 2 searches investigating the exotic jungle beyond the Standard Model | Phys. Rept. 1116 (2025) 301 | 2403.09292 |
| 4 | CMS Collaboration | Dark sector searches with the CMS experiment | Phys. Rept. 1115 (2025) 448 | CMS-EXO-23-005 2405.13778 |
| 5 | N. G. Deshpande and E. Ma | Pattern of symmetry breaking with two Higgs doublets | PRD 18 (1978) 2574 | |
| 6 | L. Lopez Honorez, E. Nezri, J. F. Oliver, and M. H. G. Tytgat | The Inert Doublet Model: an archetype for dark matter | JCAP 02 (2007) 028 | hep-ph/0612275 |
| 7 | R. Barbieri, L. J. Hall, and V. S. Rychkov | Improved naturalness with a heavy Higgs: an alternative road to LHC physics | PRD 74 (2006) 015007 | hep-ph/0603188 |
| 8 | Q.-H. Cao, E. Ma, and G. Rajasekaran | Observing the dark scalar doublet and its impact on the standard-model Higgs boson at colliders | PRD 76 (2007) 095011 | 0708.2939 |
| 9 | A. Ilnicka, M. Krawczyk, and T. Robens | Inert Doublet Model in light of LHC Run 1 and astrophysical data | PRD 93 (2016) 055026 | 1508.01671 |
| 10 | J. Kalinowski, T. Robens, D. Sokolowska, and A. F. Zarnecki | IDM benchmarks for the LHC and future colliders | Symmetry 13 (2021) 991 | 2012.14818 |
| 11 | J. Kalinowski et al. | Exploring inert scalars at CLIC | JHEP 07 (2019) 053 | 1811.06952 |
| 12 | A. F. Zarnecki et al. | Searching inert scalars at future e$ ^+ $e$ ^- $ colliders | in \it Proc. Int. Workshop on Future Linear Colliders, 2020 | 2002.11716 |
| 13 | J. Braathen, M. Gabelmann, T. Robens, and P. Stylianou | Probing the Inert Doublet Model via vector-boson fusion at a muon collider | JHEP 05 (2025) 055 | 2411.13729 |
| 14 | CLIC Collaboration | Pair-production of the charged IDM scalars at high energy CLIC | EPJC 82 (2022) 738 | 2201.07146 |
| 15 | A. Belyaev et al. | Decoding dark matter at future e$ ^+ $e$ ^- $ colliders | PRD 106 (2022) 015016 | 2112.15090 |
| 16 | Y. Guo-He et al. | Searches for dark matter via charged Higgs pair production in the Inert Doublet Model at a \ensuremath\gamma\ensuremath\gamma collider | Chin. Phys. C 45 (2021) 103101 | 2006.06216 |
| 17 | J. Kalinowski et al. | Benchmarking the Inert Doublet Model for $ e^+ e^- $ colliders | JHEP 12 (2018) 081 | 1809.07712 |
| 18 | A. Datta, N. Ganguly, N. Khan, and S. Rakshit | Exploring collider signatures of the inert Higgs doublet model | PRD 95 (2017) 015017 | 1610.00648 |
| 19 | M. Hashemi, M. Krawczyk, S. Najjari, and A. F. \.Z arnecki | Production of inert scalars at the high energy $ e^+ e^- $ colliders | JHEP 02 (2016) 187 | 1512.01175 |
| 20 | H. Abouabid et al. | One-loop radiative corrections to $ e^+ e^-\to Zh^0/H^0A^0 $ in the Inert Higgs Doublet Model | JHEP 05 (2021) 100 | 2009.03250 |
| 21 | H. Abouabid et al. | Full one-loop radiative corrections to $ e^+e^-\to H^+H^- $ in the Inert Doublet Model | PRD 109 (2024) 015009 | 2204.05237 |
| 22 | A. Bal et al. | Search for additional scalar bosons within the Inert Doublet Model in a final state with two leptons at the FCC-ee | Eur. Phys. J. C. 85 (2025) 891 | 2504.12178 |
| 23 | A. Ghosh, P. Konar, C. Sen, and B. Thacker | Illuminating degenerate dark sector of Inert Doublet Model at muon collider | 2508.06289 | |
| 24 | S. Sekmen | Supersymmetry searches in CMS Run 2: a complete review | HiHEP 1 (2025) 18 | 2510.17971 |
| 25 | D. Dercks and T. Robens | Constraining the Inert Doublet Model using vector-boson fusion | EPJC 79 (2019) 924 | 1812.07913 |
| 26 | A. Belyaev et al. | Multilepton signatures from dark matter at the LHC | JHEP 09 (2022) 173 | 2204.06411 |
| 27 | G. B é langer et al. | Dilepton constraints in the Inert Doublet Model from Run 1 of the LHC | PRD 91 (2015) 115011 | 1503.07367 |
| 28 | J. Lahiri, T. Robens, and K. Rolbiecki | Constraining the Inert Doublet Model at the LHC | 2511.23133 | |
| 29 | CMS Collaboration | HEPData record for this analysis | link | |
| 30 | I. F. Ginzburg, K. A. Kanishev, M. Krawczyk, and D. Sokolowska | Evolution of universe to the present inert phase | PRD 82 (2010) 123533 | 1009.4593 |
| 31 | A. Belyaev et al. | Advancing LHC probes of dark matter from the inert two-Higgs-doublet model with the monojet signal | PRD 99 (2019) 015011 | 1809.00933 |
| 32 | A. Belyaev et al. | Anatomy of the inert two Higgs doublet model in the light of the LHC and non-LHC dark matter searches | PRD 97 (2018) 035011 | 1612.00511 |
| 33 | A. Ilnicka, T. Robens, and T. Stefaniak | Constraining extended scalar sectors at the LHC and beyond | Mod. Phys. Lett. A 33 (2018) 1830007 | 1803.03594 |
| 34 | T. Robens | News from extended scalar sectors | in \it, 2026 Proc. Corfu Summer Institute 202 (2026) 5 |
2603.27636 |
| 35 | D. Eriksson, J. Rathsman, and O. Stal | 2HDMC: Two-Higgs-Doublet Model Calculator | Comput. Phys. Commun. 181 (2010) 833 | 0902.0851 |
| 36 | G. Altarelli and R. Barbieri | Vacuum polarization effects of new physics on electroweak processes | PLB 253 (1991) 161 | |
| 37 | M. E. Peskin and T. Takeuchi | A new constraint on a strongly interacting Higgs sector | PRL 65 (1990) 964 | |
| 38 | M. E. Peskin and T. Takeuchi | Estimation of oblique electroweak corrections | PRD 46 (1992) 381 | |
| 39 | I. Maksymyk, C. P. Burgess, and D. London | Beyond S, T and U | PRD 50 (1994) 529 | hep-ph/9306267 |
| 40 | ATLAS Collaboration | Combination of searches for invisible decays of the Higgs boson using 139 fb$ ^{-1} $ of proton-proton collision data at $ \sqrt{s}= $ 13 TeV collected with the ATLAS experiment | PLB 842 (2023) 137963 | 2301.10731 |
| 41 | G. B é langer et al. | micrOMEGAs5.0: Freeze-in | Comput. Phys. Commun. 231 (2018) 173 | 1801.03509 |
| 42 | Planck Collaboration | Planck 2018 results. VI. Cosmological parameters | [Erratum: \tt doi:10./0004-6361/33910e], 2020 Astron. Astrophys. 641 (2020) A6 |
1807.06209 |
| 43 | LZ Collaboration | Dark matter search results from 4.2 $ \text{ }\text{ }\text{Tonne}\text{-}\text{Years} $ of exposure of the LUX-ZEPLIN (LZ) experiment | PRL 135 (2025) 011802 | 2410.17036 |
| 44 | E. Lundstrom, M. Gustafsson, and J. Edsjo | The Inert Doublet Model and LEP II limits | PRD 79 (2009) 035013 | 0810.3924 |
| 45 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 46 | CMS Collaboration | Performance of the CMS high-level trigger during LHC Run 2 | JINST 19 (2024) P11021 | CMS-TRG-19-001 2410.17038 |
| 47 | CMS Collaboration | Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | JINST 15 (2020) P10017 | CMS-TRG-17-001 2006.10165 |
| 48 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 3 (2008) S08004 | 1003.4038 |
| 49 | CMS Collaboration | Development of the CMS detector for the CERN LHC Run 3 | JINST 19 (2024) P05064 | CMS-PRF-21-001 2309.05466 |
| 50 | J. Alwall et al. | The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations | JHEP 07 (2014) 079 | 1405.0301 |
| 51 | A. Goudelis, B. Herrmann, and O. St\r a l | Dark matter in the Inert Doublet Model after the discovery of a Higgs-like boson at the LHC | JHEP 09 (2013) 106 | 1303.3010 |
| 52 | J. Alwall et al. | Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions | EPJC 53 (2008) 473 | 0706.2569 |
| 53 | Y. Li and F. Petriello | Combining QCD and electroweak corrections to dilepton production in FEWZ | PRD 86 (2012) 094034 | 1208.5967 |
| 54 | R. Frederix and S. Frixione | Merging meets matching in MC@NLO | JHEP 12 (2012) 061 | 1209.6215 |
| 55 | P. Nason | A new method for combining NLO QCD with shower Monte Carlo algorithms | JHEP 11 (2004) 040 | hep-ph/0409146 |
| 56 | S. Frixione, P. Nason, and C. Oleari | Matching NLO QCD computations with parton shower simulations: the POWHEG method | JHEP 11 (2007) 070 | 0709.2092 |
| 57 | S. Alioli, P. Nason, C. Oleari, and E. Re | A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX | JHEP 06 (2010) 043 | 1002.2581 |
| 58 | T. Melia, P. Nason, R. Rontsch, and G. Zanderighi | $ {\mathrm{W}^{+}\mathrm{W}^{-}} $, $ {\mathrm{W}\mathrm{Z}} $ and $ {\mathrm{Z}\mathrm{Z}} $ production in the POWHEG BOX | JHEP 11 (2011) 078 | 1107.5051 |
| 59 | J. M. Campbell and R. K. Ellis | MCFM for the Tevatron and the LHC | Nucl. Phys. B Proc. Suppl. 205-206 10, 2010 link |
1007.3492 |
| 60 | J. M. Campbell, R. K. Ellis, P. Nason, and E. Re | Top-pair production and decay at NLO matched with parton showers | JHEP 04 (2015) 114 | 1412.1828 |
| 61 | S. Alioli, P. Nason, C. Oleari, and E. Re | NLO single-top production matched with shower in POWHEG: \textits- and \textitt-channel contributions | [Erratum: \tt doi:10./JHEP02()011], 2009 JHEP 09 (2009) 111 |
0907.4076 |
| 62 | E. Re | Single-top $ {\mathrm{W}} $t-channel production matched with parton showers using the POWHEG method | EPJC 71 (2011) 1547 | 1009.2450 |
| 63 | M. Czakon and A. Mitov | Top++: a program for the calculation of the top-pair cross section at hadron colliders | Comput. Phys. Commun. 185 (2014) 2930 | 1112.5675 |
| 64 | J. Campbell, T. Neumann, and Z. Sullivan | Single-top-quark production in the $ t $-channel at NNLO | JHEP 02 (2021) 040 | 2012.01574 |
| 65 | N. Kidonakis and N. Yamanaka | Higher-order corrections for $ tW $ production at high-energy hadron colliders | JHEP 05 (2021) 278 | 2102.11300 |
| 66 | NNPDF Collaboration | Parton distributions for the LHC Run II | JHEP 04 (2015) 040 | 1410.8849 |
| 67 | T. Sjöstrand et al. | An introduction to PYTHIA 8.2 | Comput. Phys. Commun. 191 (2015) 159 | 1410.3012 |
| 68 | C. Bierlich et al. | A comprehensive guide to the physics and usage of PYTHIA 8.3 | SciPost Phys. Codeb. 8 (2022) | 2203.11601 |
| 69 | CMS Collaboration | Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements | EPJC 80 (2020) 4 | CMS-GEN-17-001 1903.12179 |
| 70 | GEANT4 Collaboration | GEANT 4---a simulation toolkit | NIM A 506 (2003) 250 | |
| 71 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 72 | CMS Collaboration | Technical proposal for the Phase-II upgrade of the Compact Muon Solenoid | CMS Technical Proposal CERN-LHCC-2015-010, CMS-TDR-15-02, 2015 CDS |
|
| 73 | CMS Collaboration | Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC | JINST 16 (2021) P05014 | CMS-EGM-17-001 2012.06888 |
| 74 | CMS Collaboration | Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s}= $ 13 TeV | JINST 13 (2018) P06015 | CMS-MUO-16-001 1804.04528 |
| 75 | M. Cacciari, G. P. Salam, and G. Soyez | The anti-$ k_{\mathrm{T}} $ jet clustering algorithm | JHEP 04 (2008) 063 | 0802.1189 |
| 76 | M. Cacciari, G. P. Salam, and G. Soyez | FastJet user manual | EPJC 72 (2012) 1896 | 1111.6097 |
| 77 | CMS Collaboration | Pileup mitigation at CMS in 13 TeV data | JINST 15 (2020) P09018 | CMS-JME-18-001 2003.00503 |
| 78 | D. Bertolini, P. Harris, M. Low, and N. Tran | Pileup Per Particle Identification | JHEP 10 (2014) 059 | 1407.6013 |
| 79 | CMS Collaboration | Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV | JINST 12 (2017) P02014 | CMS-JME-13-004 1607.03663 |
| 80 | CMS Collaboration | Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector | JINST 14 (2019) P07004 | CMS-JME-17-001 1903.06078 |
| 81 | E. Bols et al. | Jet flavour classification using DeepJet | JINST 15 (2020) P12012 | 2008.10519 |
| 82 | P. Baldi et al. | Parameterized neural networks for high-energy physics | EPJC 76 (2016) 235 | 1601.07913 |
| 83 | C. G. Lester and A. J. Barr | mTGen: mass scale measurements in pair-production at colliders | JHEP 12 (2007) 102 | |
| 84 | C. G. Lester | The stransverse mass, $ m_{T2} $, in special cases | JHEP 05 (2011) 076 | 1103.5682 |
| 85 | R. Mahbubani, K. T. Matchev, and M. Park | Re-interpreting the oxbridge stransverse mass variable $ m_{T2} $ in general cases | JHEP 03 (2013) 134 | 1212.1720 |
| 86 | CMS Collaboration | Search for physics beyond the standard model in events with a Z boson, jets, and missing transverse energy in pp collisions at $ \sqrt{s}= $ 7 TeV | PLB 716 (2012) 260 | CMS-SUS-11-021 1204.3774 |
| 87 | T. Chen and C. Guestrin | XGBoost: a scalable tree boosting system | in \it nd ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, 2016 Proc. 2 (2016) 785 |
1603.02754 |
| 88 | A. Paszke et al. | PyTorch: an imperative style, high-performance deep learning library | 1912.01703 | |
| 89 | D.-A. Clevert, T. Unterthiner, and S. Hochreiter | Fast and accurate deep network learning by Exponential Linear Units (ELUs) | link | 1511.07289 |
| 90 | D. Kingma and J. Ba | Adam: a method for stochastic optimization | in \it Proc. Int. Conf. on Learning Representations. 201 (1900) 4 |
1412.6980 |
| 91 | J. Terven et al. | A comprehensive survey of loss functions and metrics in deep learning | \hrefhttp://www.arXiv.org/abs/2307.02694v5\textttarXiv:2307.02694v5, 2025 Artif. Intell. Rev. 58 (2025) 195 |
|
| 92 | S. Rippa | An algorithm for selecting a good parameter $ c $ in radial basis function interpolation | Adv. Comput. Math. 11 (1999) 193 | |
| 93 | CMS Collaboration | Search for dark matter produced in association with a leptonically decaying Z boson in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | [Erratum: Eur.Phys.J.C 81, 333 ()], 2021 EPJC 81 (2021) 13 |
CMS-EXO-19-003 2008.04735 |
| 94 | CMS Collaboration | Search for physics beyond the standard model in dilepton mass spectra in proton-proton collisions at $ \sqrt{s}= $ 8 TeV | JHEP 04 (2015) 025 | CMS-EXO-12-061 1412.6302 |
| 95 | CMS Collaboration | Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV | JINST 13 (2018) P05011 | CMS-BTV-16-002 1712.07158 |
| 96 | CMS Collaboration | Measurement of the inelastic proton-proton cross section at $ \sqrt{s}= $ 13 TeV | JHEP 07 (2018) 161 | CMS-FSQ-15-005 1802.02613 |
| 97 | CMS Collaboration | Precision luminosity measurement in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS | EPJC 81 (2021) 800 | CMS-LUM-17-003 2104.01927 |
| 98 | CMS Collaboration | CMS luminosity measurement for the 2017 data-taking period at $ \sqrt{s} = $ 13 TeV | CMS Physics Analysis Summary, 2018 CMS-PAS-LUM-17-004 |
CMS-PAS-LUM-17-004 |
| 99 | CMS Collaboration | CMS luminosity measurement for the 2018 data-taking period at $ \sqrt{s} = $ 13 TeV | CMS Physics Analysis Summary, 2019 CMS-PAS-LUM-18-002 |
CMS-PAS-LUM-18-002 |
| 100 | CMS Collaboration | Luminosity measurement in proton-proton collisions at 13.6 TeV in 2022 at CMS | CMS Physics Analysis Summary, 2024 CMS-PAS-LUM-22-001 |
CMS-PAS-LUM-22-001 |
| 101 | J. Butterworth et al. | PDF4LHC recommendations for LHC Run II | JPG 43 (2016) 023001 | 1510.03865 |
| 102 | R. D. Ball et al. | The PDF4LHC21 combination of global PDF fits for the LHC Run III* | JPG 49 (2022) 080501 | 2203.05506 |
| 103 | R. Barlow and C. Beeston | Fitting using finite Monte Carlo samples | Comput. Phys. Commun. 77 (1993) 219 | |
| 104 | CMS Collaboration | The CMS statistical analysis and combination tool: COMBINE | Comput. Softw. Big Sci. 8 (2024) 19 | CMS-CAT-23-001 2404.06614 |
| 105 | G. Cowan, K. Cranmer, E. Gross, and O. Vitells | Asymptotic formulae for likelihood-based tests of new physics | [Erratum: \tt doi:10.1140/epjc/s2-013-2501-z], 2011 EPJC 71 (2011) 1554 |
1007.1727 |
| 106 | T. Junk | Confidence level computation for combining searches with small statistics | NIM A 434 (1999) 435 | hep-ex/9902006 |
| 107 | A. L. Read | Presentation of search results: the $ \text{CL}_\text{s} $ technique | JPG 28 (2002) 2693 | |
|
|
Compact Muon Solenoid LHC, CERN |
|
|
|
|
|
|