- The paper presents the first detector-level, background-inclusive study of soft opposite-sign dimuons plus missing energy from two-component scalar dark matter in the I(2+1)HDM, using a hard ISR jet to trigger events.
- The analysis reduces collider phenomenology to dark-matter masses and mass splittings, predicts a distinctive double-bump dimuon spectrum, and uses a soft Mₜ₂ requirement to suppress tau-pair backgrounds by nearly a factor of 30.
- The benchmark yields S/√B = 1.35 with 300 fb⁻¹ at 13.6 TeV and 4.93 with 4 ab⁻¹ at the HL-LHC under statistical-only assumptions, although systematic uncertainties and the loss of the double-bump feature remain important limitations.
Overview and motivation
This paper investigates the collider phenomenology of a two-component scalar dark matter (DM) scenario at the LHC, focusing on the opposite-sign dimuon (μ+μ−) plus missing transverse energy (ETmiss) final state accompanied by a hard jet from initial-state radiation (ISR). The defining feature of the signal is a soft dimuon system whose invariant mass lies well below mZ, arising from the decay of an off-shell Z boson in the cascade of each dark sector. The analysis is conducted within the Inert (2+1) Higgs Doublet Model (I(2+1)HDM), a 3-Higgs Doublet Model with one active doublet and two inert doublets, stabilised by a Z2×Z2′ symmetry that renders the lightest neutral scalar from each inert doublet stable (2607.00243).
The motivation for considering two DM components is twofold. First, multi-component WIMP sectors can produce collider signatures qualitatively distinct from single-component scenarios, since several dark states with different masses and mass splittings contribute simultaneously to the same final state. Second, while previous studies of the I(2+1)HDM had noted characteristic distribution shapes at the LHC, no detector-level analysis including Standard Model (SM) backgrounds and a dedicated event selection had been performed for this soft-dimuon topology.
Model structure and parameter mapping
The I(2+1)HDM scalar potential is invariant under Z2×Z2′, under which only ϕ1 (ϕ2) is odd under Z2 (Z2′), while all SM fields and ETmiss0 are even. Only ETmiss1 acquires a vacuum expectation value, yielding a SM-like 125 GeV Higgs boson and a Type-I Yukawa structure free of tree-level flavour-changing neutral currents. The physical spectrum of each inert sector comprises a CP-even scalar ETmiss2, a CP-odd scalar ETmiss3, and charged scalars ETmiss4, with ETmiss5 enforced by quartic-coupling sign conditions.
A key methodological contribution is the reduction of the model's collider-relevant parameter space to two quantities per sector: the DM mass ETmiss6 and the mass splitting ETmiss7. Since the ETmiss8 coupling is fixed by electroweak gauge interactions, these masses determine both the production kinematics and the kinematic endpoint of the dimuon invariant-mass spectrum, ETmiss9. Two sectors with different mZ0 therefore generate a double-bump structure in the dimuon invariant-mass distribution — the characteristic feature distinguishing the two-component scenario from a single-component inert scalar model. This parametrisation makes the analysis applicable beyond the specific model, to any weakly interacting sector with analogous electroweak associated production and cascade decays through an off-shell mZ1.
Constraints and benchmark selection
The parameter scan imposes vacuum stability, perturbative unitarity, agreement with electroweak precision observables (via the oblique parameters mZ2), LEP bounds (including the mZ3-boson width constraint mZ4 and LEP-II reinterpretations excluding mZ5 GeV, mZ6 GeV, mZ7 GeV simultaneously), charged-scalar mass limits, Higgs signal-strength and invisible-decay limits (BRmZ8 from ATLAS), and DM constraints: the Planck relic density as an upper bound, with direct-detection rates rescaled by mZ9 and indirect-detection rates by Z0.
Notably, unlike single-Z1 models, the Z2 structure permits cancellations between the two sectors' contributions to Z3 and Z4, relaxing the mass-ordering constraints typical of the Inert Doublet Model. The selected benchmark BP1 has Z5 GeV, Z6 GeV, with splittings Z7 GeV and Z8 GeV. The benchmark is underabundant (Z9, Z2×Z2′0), so it is interpreted as a subdominant two-component DM scenario; the authors note that regions reproducing the full observed abundance generally involve masses and compressed spectra less favourable for the present search. The collider analysis itself, however, is independent of the cosmological abundance.
Collider analysis
Signal events are generated at leading order with CalcHEP and MadGraph5_aMC@NLO, showered with Pythia, and passed through Delphes detector simulation within CheckMATE using ATLAS 13 TeV parametrisation. The dominant backgrounds are Drell–Yan Z2×Z2′1 (29,100 fb at generator level), Z2×Z2′2, semi-muonic Z2×Z2′3, Z2×Z2′4, diboson production, Z2×Z2′5, and fake non-prompt (FNP) muons from heavy-flavour decays — the latter estimated using ATLAS Open Data Z2×Z2′6jets samples rather than computationally expensive simulation, an approach whose modelling uncertainty must be addressed in a full experimental analysis.
The eleven-cut selection includes a Z2×Z2′7-veto, Z2×Z2′8 GeV, hard leading-jet requirements (Z2×Z2′9 GeV), azimuthal cuts against Drell–Yan mismeasurement, a collinear approximation reconstruction of Z2×Z2′0, and two Z2×Z2′1 requirements. A methodological highlight is the repurposing of the standard Z2×Z2′2 variable: whereas hard cuts on this quantity are conventionally used to suppress Z2×Z2′3 and Z2×Z2′4 backgrounds in electroweakino searches with large chargino–neutralino mass splittings, here a deliberately soft cut (Z2×Z2′5 GeV) exploits the signal topology in which both muons originate from the same parent, reducing the Z2×Z2′6 background by a factor just under 30.
Results
For BP1 at Z2×Z2′7 TeV:
| Quantity |
Run 3 (300 fb⁻¹) |
HL-LHC (4 ab⁻¹, extrapolated) |
| Signal events |
Z2×Z2′8 |
Z2×Z2′9 |
| Background events |
ϕ10 |
ϕ11 |
| ϕ12 |
ϕ13 |
— |
| ϕ14 |
1.35 |
4.93 |
The HL-LHC figure is a statistical-only extrapolation; the authors state plainly that a robust discovery-level conclusion would require dedicated treatment of dominant background systematics. A naive ATLAS–CMS combination would give 6.97, but this does not constitute an experimental combination.
Before full selection, the signal exhibits the double-bump structure in ϕ15 characteristic of two independent dark sectors. However, after the inclusive-optimised cuts, this feature is not retained with sufficient significance, so establishing experimentally that the signal originates from two DM components remains difficult with this selection. The authors identify more sophisticated signal-selection strategies as necessary future work for resolving this ambiguity.
A generic scan over ϕ16 shows that a statistical-only significance of approximately 3–5 at the HL-LHC is achievable over a significant region of parameter space surviving LEP constraints, motivating dedicated experimental searches for this topology.
Limitations and open questions
Several limitations qualify the results. The benchmark is underabundant, so the analysis constrains only subdominant DM components in its most favourable region; fully abundant points tend to have heavier or more compressed spectra with reduced soft-muon acceptance. The FNP background estimate relies on simulated samples and ATLAS Open Data rather than data-driven methods, introducing modelling uncertainties not propagated into the quoted significances. All significances are statistical-only, omitting systematic uncertainties on the dominant backgrounds. Finally, the central open question left by the paper is whether an alternative event selection can preserve the double-bump structure with sufficient significance to demonstrate the two-component origin of the signal at the detector level.
Conclusion
This work provides the first detector-level, background-inclusive analysis of the soft-dimuon plus missing-energy signature of two-component scalar DM, using the I(2+1)HDM as a concrete realisation. It demonstrates that a tailored cut-based selection — notably featuring a repurposed soft ϕ17 requirement — yields ϕ18 at Run 3 luminosity and statistically significant sensitivity approaching discovery level at the HL-LHC for the chosen benchmark. While the double-bump diagnostic of two-component DM is visible pre-selection but diluted by the optimised cuts, the analysis establishes the viability of probing multi-component inert scalar sectors via soft leptons and offers a transferable strategy applicable to other weakly interacting dark sectors with off-shell ϕ19 cascade topologies.
