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arxiv: 2607.00243 · v1 · pith:L47JXBTTnew · submitted 2026-06-30 · ✦ hep-ph

Soft-Dimuon Signature from Two-Component Scalar Dark Matter at the LHC

Alexander Belyaev , Manimala Chakraborti , Shu Chen , Atri Dey , Venus Keus , Rakhi Mahbubani , Stefano Moretti This is my paper

Pith reviewed 2026-07-02 18:12 UTC · model grok-4.3

classification ✦ hep-ph
keywords dark matterLHCscalar dark matterdimuonmissing transverse energyHiggs doublet modeltwo-component dark matteroff-shell Z
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0 comments X

The pith

LHC can search for two-component scalar dark matter via soft opposite-sign dimuons plus missing energy and a hard jet.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper maps the collider reach for a two-component scalar dark matter model realized in a three-Higgs-doublet setup with two inert sectors. Each sector supplies a stable neutral scalar dark matter candidate whose partner state lies less than the Z mass away and therefore decays through an off-shell Z, yielding a soft muon pair. A Monte Carlo study designs a cut-based selection on the opposite-sign dimuon plus missing transverse energy plus hard-jet final state. For one benchmark the expected statistical-only significance is 1.35 at 300 fb inverse at Run 3 and rises to 4.93 when extrapolated to 4 ab inverse. The analysis remains valid even if the dark matter is only a subdominant component of the total relic density.

Core claim

In the I(2+1)HDM with Z2 times Z2 prime symmetry the two inert doublets each stabilize their lightest neutral scalar as a dark matter candidate. The next-to-lightest scalars in each sector decay to the dark matter plus an off-shell Z that produces a soft opposite-sign muon pair. A dedicated cut-based analysis on the dimuon plus missing transverse energy plus jet channel yields S over B approximately 9.8 percent and S over square root of B equal to 1.35 at 300 fb inverse for a representative benchmark, increasing to 4.93 at 4 ab inverse under statistical-only extrapolation. The double-bump structure visible in the dimuon invariant-mass distribution before the final cuts is not statistically r

What carries the argument

Two inert scalar doublets, each stabilized by an independent Z2 symmetry, with small mass splittings to their next-to-lightest states that enable off-shell Z decays to soft muon pairs.

If this is right

  • The parameter space is explored in terms of the two dark matter masses and the two independent mass splittings to the next-to-lightest states.
  • Before the final selection the two dark sectors produce a double-bump feature in the dimuon invariant-mass spectrum.
  • The benchmark point is underabundant and can be interpreted as subdominant dark matter while the collider analysis stays independent of cosmological abundance.
  • The same signal topology and cuts apply to any weakly interacting sector that features electroweak associated production followed by cascade decays through an off-shell Z.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Observation of the soft dimuon signal would point to the existence of multiple independent stabilizing symmetries rather than a single dark sector.
  • Combining the dimuon channel with direct detection or relic-density constraints could test whether both components contribute measurably to the total dark matter density.
  • The same off-shell Z mechanism could be searched for in models with additional inert doublets or singlets provided the mass splittings remain below m_Z.
  • Higher-luminosity runs or improved muon resolution could make the double-bump feature statistically significant and thereby distinguish two-component from single-component scenarios.

Load-bearing premise

The mass splittings between each dark matter candidate and its next-to-lightest partner must be smaller than the Z boson mass so that the partner decays through an off-shell Z.

What would settle it

A search at the LHC collecting 300 fb inverse that observes no excess above background in the soft opposite-sign dimuon plus missing transverse energy plus hard jet channel with the predicted kinematics would exclude the benchmark at the quoted significance.

Figures

Figures reproduced from arXiv: 2607.00243 by Alexander Belyaev, Atri Dey, Manimala Chakraborti, Rakhi Mahbubani, Shu Chen, Stefano Moretti, Venus Keus.

Figure 1
Figure 1. Figure 1: Diagrams leading to the µ +µ − + E/T final state mediated by an off-shell Z boson. The additional hard ISR jet required in the analysis is not shown. searching for DM has been studied previously in Ref. [9], while for the case of LHC experiments this has been done in Refs. [10, 11]. In particular, Refs. [10, 11] have pointed out that the presence of two DM candidates leads to specific shapes in the distrib… view at source ↗
Figure 2
Figure 2. Figure 2: The normalised distribution of the missing transverse energy E/T (left) and ∆R(µ −µ +) (right) after the pre-selection cuts and the requirement of OS muons and b-veto. The cutflow corresponding to the selection cuts 1–11 for our chosen BP is listed in Tab. 3 while the significance values for LHC Run 3 and HL-LHC are listed in Tab. 4. For the nominal signal region, we obtain S/B ≃ 9.8% and S/√ B = 1.35 at L… view at source ↗
Figure 3
Figure 3. Figure 3: The normalised distribution of the transverse momentum of the leading jet (left) and ∆ϕ between the leading jet and E/T (right) after the pre-selection cuts and the requirement of OS muons and b-veto. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The normalised distribution of the mτ+τ− (left) and MT2(µ +, µ−, E/T ) (right) after the pre-selection cuts and the requirement of OS muons and b-veto. Z-boson width excludes the region MH1 + MA1 < MZ [59], while the LEP-II reinterpretation excludes points for which MA1 ≤ 100 GeV, MH1 ≤ 80 GeV and ∆M ≥ 8 GeV are simultaneously satisfied [21]. From the plots it is clear that a statistical-only significance … view at source ↗
Figure 5
Figure 5. Figure 5: The normalised distribution of the dimuon invariant mass (left) and MT2(µ1+j, µ2+j, E/T ) (right) after the pre-selection cuts and the requirement of OS muons and b-veto. At this preselection level, note the double-bump structure in the dimuon invariant-mass distribution for the signal, the observation of which would be a smoking gun for the presence of two distinct DM sectors with independent masses and m… view at source ↗
Figure 6
Figure 6. Figure 6: Cross sections, efficiencies and significances at the LHC with √ s = 13.6 TeV over the I(2+1)HDM parameter space, mapped in terms of absolute mass of the DM candidate and the mass difference between this and the next-to-lightest neutral inert state Subplot(a) also shows the explicit mass values chosen for BP1 for the first [red point] and second [yellow point] inert doublet. Significance values in subplot … view at source ↗
read the original abstract

We explore the potential of the Large Hadron Collider to probe a two-component scalar dark matter scenario in the opposite-sign dimuon plus missing transverse energy final state, accompanied by a hard jet. The signal features a soft dimuon system with an invariant mass well below $m_Z$. We consider a 3-Higgs Doublet Model with one active and two inert scalar doublets, where a $Z_2 \times Z_2'$ symmetry stabilises the lightest neutral scalar in each inert sector, yielding two scalar DM candidates. The relevant parameter space is mapped in terms of the two DM masses and the mass splittings between each DM candidate and its corresponding next-to-lightest scalar state. We perform a detector-level Monte Carlo analysis and design a dedicated cut-based selection, including a transverse-mass requirement adapted to the signal topology. For a representative benchmark, we obtain $S/B\simeq 9.8%$ and a statistical-only significance of $S/\sqrt{B}=1.35$ at Run 3 with ${\cal L}=300~{\rm fb}^{-1}$, increasing to $S/\sqrt{B}=4.93$ under a statistical-only extrapolation to ${\cal L}=4~{\rm ab}^{-1}$. Before the full selection, the two dark sectors generate a double-bump structure in the dimuon invariant-mass distribution. After the cuts optimised for inclusive sensitivity, however, this feature is not statistically robust enough to establish the two-component origin of the signal. The benchmark is underabundant and is interpreted as a subdominant two-component DM scenario, while the collider analysis remains independent of its cosmological abundance. Although the numerical study is carried out in the I(2+1)HDM, the results are applicable to weakly interacting sectors with similar electroweak associated production and cascade decays, where a heavier state separated from the DM candidate by less than $m_Z$ produces a soft muon pair via an off-shell $Z$ boson.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript explores the LHC sensitivity to a two-component scalar dark matter scenario in the I(2+1)HDM via the soft opposite-sign dimuon + MET + hard jet final state. The signal arises from cascade decays of next-to-lightest scalars through off-shell Z bosons when mass splittings are below m_Z. Parameter space is mapped in the two DM masses and splittings; a cut-based detector-level MC analysis is performed, yielding for one benchmark S/B ≃ 9.8 % and statistical-only significances S/√B = 1.35 (300 fb^{-1}) and 4.93 (4 ab^{-1}). The double-bump feature in m_μμ is noted to lose statistical robustness after cuts, and the benchmark is interpreted as subdominant DM.

Significance. If the analysis holds after inclusion of systematics and background validation, the work supplies a concrete, topology-adapted search strategy for two-component scalar DM with soft dimuon signatures that can be ported to other weakly coupled electroweak sectors. The modest S/B and purely statistical significances limit the immediate phenomenological impact.

major comments (2)
  1. [Abstract] Abstract: the reported significances are explicitly statistical-only (S/√B = 1.35 at 300 fb^{-1} and 4.93 at 4 ab^{-1}); the absence of any systematic uncertainties, background estimation/validation procedure, or full cut-optimization details is load-bearing for the central claim that the LHC can probe this scenario.
  2. [Abstract] Abstract: the double-bump structure generated by the two dark sectors before cuts is stated to be 'not statistically robust enough' after the inclusive selection; this directly weakens any claim that the signature can establish the two-component nature of the signal.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported significances are explicitly statistical-only (S/√B = 1.35 at 300 fb^{-1} and 4.93 at 4 ab^{-1}); the absence of any systematic uncertainties, background estimation/validation procedure, or full cut-optimization details is load-bearing for the central claim that the LHC can probe this scenario.

    Authors: We agree that the statistical-only nature of our significances and the lack of systematic uncertainties are important caveats for the phenomenological claim. Although the abstract already notes that the significances are statistical-only, we will revise it to more explicitly state that no systematic uncertainties have been included and that a complete experimental analysis would require background validation and systematic error estimation. The cut-optimization details are provided in the main text of the manuscript. We will update the abstract in the revised version. revision: yes

  2. Referee: [Abstract] Abstract: the double-bump structure generated by the two dark sectors before cuts is stated to be 'not statistically robust enough' after the inclusive selection; this directly weakens any claim that the signature can establish the two-component nature of the signal.

    Authors: The manuscript already acknowledges this limitation in the abstract by stating that the double-bump feature is not statistically robust enough after the cuts to establish the two-component origin of the signal. Our central claim concerns the LHC sensitivity to the soft dimuon signature from the two-component scalar DM scenario, not the ability to confirm the two-component nature via the invariant mass distribution. We believe the text does not overstate the latter point, so no revision is required. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central results (S/B ≃ 9.8% and statistical significances) are obtained from a standard detector-level Monte Carlo simulation of a benchmark point in the I(2+1)HDM, with explicit input parameters for the two DM masses and mass splittings. The cut-based analysis and transverse-mass requirement are applied to simulated events; the signal topology is defined by the stated mass-splitting regime (< m_Z) rather than derived from the outputs. No equations reduce predictions to fitted inputs by construction, no self-citation chains support the core claim, and the collider study is explicitly independent of cosmological abundance. This is a conventional model-prediction exercise with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the 3HDM extension with Z2 x Z2' symmetries that stabilize two scalar DM candidates and on the accuracy of MC modeling of signal and backgrounds; the benchmark point is chosen by hand within the mapped parameter space.

free parameters (2)
  • two DM masses
    The masses of the two scalar DM candidates are free parameters used to define the benchmark point.
  • mass splittings
    The mass differences to the next-to-lightest states in each sector are free parameters that control the softness of the dimuon system.
axioms (1)
  • domain assumption Z_2 × Z_2' symmetry stabilizes the lightest neutral scalars in each inert doublet
    Invoked to ensure both scalars are stable DM candidates (abstract: 'a Z_2 × Z_2' symmetry stabilises the lightest neutral scalar in each inert sector')
invented entities (1)
  • Two inert scalar doublets no independent evidence
    purpose: To furnish two stable scalar DM candidates in addition to the active Higgs doublet
    Postulated as part of the 3HDM extension; no independent evidence provided outside the model assumptions.

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