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REVIEW 2 major objections 4 minor 35 references

Yukawa-driven fermion portals keep singlet scalar dark matter viable; muon colliders can discover the charged partners into the multi-TeV range.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-12 00:01 UTC pith:QP6TLWE6

load-bearing objection Solid update of the authors’ own fermion-portal scalar DM model under 2025 LZ limits, plus the first detector-level muon-collider projections for the lightest charged VL fermion; useful for the subfield, not a new framework. the 2 major comments →

arxiv 2607.03775 v1 pith:QP6TLWE6 submitted 2026-07-04 hep-ph

Probing Fermion-Portal Scalar Dark Matter through Charged Vector-Like Fermions at Future Muon Colliders

Songshaptak De , Tapoja Jha , Najimuddin Khan , Madhurima Pandey This is my paper
classification hep-ph
keywords scalar dark matterfermion portalvector-like fermionsmuon colliderrelic densitydirect detectionYukawa annihilationmissing energy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Latest direct-detection limits have squeezed the usual Higgs-portal coupling of a real singlet scalar dark matter particle almost out of existence, leaving only a narrow resonance window. This paper shows that the same model, once equipped with Z2-odd vector-like charged fermions, recovers a broad viable mass range: the new Yukawa couplings open t- and u-channel annihilations and co-annihilations that set the observed relic density while the Higgs portal stays small enough to satisfy current direct-detection bounds. The same charged fermions are then pair-produced at proposed muon colliders. A full detector-level study of the clean e+e-+missing-energy final state demonstrates that a 3 TeV machine with 1 ab−1 can discover the lightest charged state up to about 1.5 TeV, while a 10 TeV machine with 10 ab−1 reaches roughly 2 TeV—covering nearly the entire dark-matter-favored parameter space and far surpassing the projected HL-LHC reach.

Core claim

In a minimal fermion-portal extension of real-singlet scalar dark matter, Yukawa-driven t- and u-channel annihilations and co-annihilations involving the new vector-like charged fermions can reproduce the observed relic abundance over a wide mass range while remaining consistent with the latest direct-detection limits; future muon colliders can then discover the lightest charged fermion up to multi-TeV masses in the e+e-+MET channel, covering essentially the entire dark-matter-allowed region.

What carries the argument

The fermion-portal Yukawa couplings that open t- and u-channel annihilations of the singlet scalar into SM leptons (and co-annihilations with the Z2-odd fermions), which set the relic density once the Higgs portal is forced small by direct detection.

Load-bearing premise

The analysis forces the new Yukawa couplings almost entirely into the electron generation and keeps the fermion mixing angle tiny, so that muon g-2 and flavor-violation bounds are automatically satisfied while a clean electron-channel collider signal remains available.

What would settle it

A null result for e+e-+MET at a 10 TeV muon collider with 10 ab−1, combined with continued non-observation of the same final state at the HL-LHC, would exclude the multi-TeV charged-fermion masses that the paper claims are both dark-matter viable and discoverable.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The pure Higgs-portal singlet is essentially ruled out except near the 62 GeV resonance; any surviving singlet scalar dark matter must rely on additional portals such as the fermion channels studied here.
  • A 3 TeV muon collider already discovers charged fermions up to ~1.5 TeV across most of the dark-matter-allowed strip; a 10 TeV machine covers nearly the entire strip up to ~2 TeV.
  • The same parameter space that yields the correct relic density is directly testable in a single clean final state, turning the model into a high-priority target for next-generation lepton colliders.
  • HL-LHC coverage remains limited to roughly 1 TeV, so muon colliders become the decisive probe for the heavier, co-annihilation-dominated regime.

Where Pith is reading between the lines

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

  • If the flavor structure is forced more democratic by other ultraviolet constraints, the electron-channel purity assumed here would degrade and both the relic-density calculation and the collider signal would need re-evaluation.
  • The same clean missing-energy signature could be searched for at a future high-energy e+e− collider, providing an independent cross-check of the muon-collider reach.
  • Successful discovery of the charged fermions would immediately fix the mass splitting and Yukawa strength, allowing a sharp prediction for the residual direct-detection rate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper revisits a Z2-stabilized fermion-portal scalar dark-matter model with a real singlet scalar S and vector-like charged singlet and doublet fermions. After showing that the latest LZ direct-detection bounds force the Higgs-portal coupling κ to be tiny, the authors demonstrate that Yukawa-driven t- and u-channel annihilations (and co-annihilations) involving the new fermions can still reproduce the observed relic density over a wide mass range while remaining consistent with vacuum stability, unitarity, LFV, (g-2), and Higgs invisible-decay constraints. They then perform a detector-level study of the process μ+μ- o E1+E1- o e+e- + MET at future muon colliders (√s = 3 TeV, 1 ab-1 and 10 TeV, 10 ab-1), finding 5σ discovery reaches of approximately 1.5 TeV and 2 TeV, respectively, that cover most of the dark-matter-favored parameter space.

Significance. If the results hold, the work supplies a concrete, experimentally testable realization of fermion-portal scalar dark matter that survives present direct-detection limits and is largely accessible at proposed muon colliders. The combination of a full relic-density scan (micrOMEGAs + SARAH/SPheno) with a realistic Delphes-based muon-collider analysis (three cut categories, 10 % systematics) is a useful benchmark for both the dark-matter and collider communities. The explicit mapping of the green DM-allowed band onto the projected 2σ/5σ contours (Figs. 11–12) makes the complementarity claim falsifiable and therefore valuable.

major comments (2)
  1. The electron-only Yukawa restriction (Yf1 = 0.3, Yf2,f3 ∼ 0, Y'fi = 0, cos β = 0.995) is applied uniformly to both the relic-density scan (Sec. III, Tables I–II, Figs. 4–5) and the collider analysis (Sec. IV.A). While this choice is required by existing LFV and (g-2)μ bounds (Sec. II.B), the manuscript never quantifies how much the green DM-allowed band or the 1.5–2 TeV reach would shrink if a more democratic flavor structure or a larger mixing angle were allowed. A short sensitivity study (or an explicit statement that the quoted reaches apply only under this flavor ansatz) is needed for the central claim to be fully robust.
  2. In the pure Higgs-portal benchmarks of Table I the authors set ME1 = ME2 = 2.5 TeV and Yf = 0, yet the subsequent Yukawa-driven scan (Fig. 4) fixes ME1 = 2 TeV, ME2 = 3 TeV. The text does not demonstrate that the qualitative conclusion—that t/u-channel annihilations open a wide allowed window—is independent of this particular mass hierarchy. A brief check with a different hierarchy (or a statement that the hierarchy is fixed by the collider reach) would remove residual doubt about the generality of the relic-density result.
minor comments (4)
  1. Fig. 5 caption states “Yf = 0.3 (left) and Yf = 0.3 (right)”; the right panel is intended to be Yf = 0.4.
  2. The significance formula (Eq. 4.1) is standard, but the choice of a flat 10 % systematic is never justified against expected muon-collider systematics; a one-sentence reference would help.
  3. Several sentences in the Introduction and Conclusion contain minor grammatical slips (“despite of being successful”, “we, however, find astrophysical evidence”) that should be polished.
  4. The kinematic boundary MS < ME1 is shaded in Fig. 7 but never explicitly labeled; a short legend entry would improve readability.

Circularity Check

0 steps flagged

No significant circularity: relic density and collider reach are computed from external benchmarks and standard tools; only minor reuse of authors' prior model Lagrangian.

full rationale

The paper's central results (viable DM parameter space via Yukawa t/u-channel annihilation matching Planck Ωh² while satisfying LZ DD limits, and projected 5σ muon-collider reach to ~1.5–2 TeV) are obtained by scanning free parameters (MDM, κ, Yf, ME1) against external experimental inputs and by running a standard MadGraph+Pythia+Delphes pipeline with SM backgrounds. The model Lagrangian is taken from the authors' earlier works, but those citations supply only the field content and interaction terms; the numerical relic-density, direct-detection, LFV and collider calculations are redone with current data and do not reduce by construction to any fitted quantity or self-referential uniqueness claim. No prediction is forced by a prior fit, no uniqueness theorem is imported, and no ansatz is smuggled via citation. The single minor self-referential element (reuse of the Z2-odd singlet-doublet fermion setup) is independently re-constrained and does not load-bear the new claims. Score 1 reflects only that routine model reuse.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 2 invented entities

The central claims rest on a standard Z2-stabilized scalar + vector-like fermion extension, external experimental numbers (Planck relic density, LZ SI cross-section, MEG LFV bound), and a handful of free parameters (masses, κ, Y_f) that are scanned rather than derived. No new force or conserved charge is invented beyond the usual discrete symmetry.

free parameters (4)
  • Higgs-portal coupling κ
    Scanned 0 ≤ κ ≤ 0.15; upper edge set by direct-detection exclusion for multi-TeV DM.
  • Yukawa coupling Y_f (electron generation)
    Scanned 0–0.5; values ~0.35–0.45 required for correct relic density once κ is suppressed.
  • Charged-fermion masses M_E1, M_E2 and DM mass M_s
    Free mass parameters varied over multi-TeV ranges subject only to kinematic and unitarity bounds.
  • Mixing angle cos β = 0.995
    Fixed by hand to satisfy electroweak precision constraints while keeping the lightest charged state mostly doublet-like.
axioms (3)
  • domain assumption Discrete Z2 symmetry under which the new scalar and fermions are odd, guaranteeing DM stability and forbidding mixing with SM fermions.
    Standard assumption of the scotogenic/fermion-portal literature; invoked from the Lagrangian definition in Sec. II.
  • domain assumption Absolute stability and perturbative unitarity of the scalar potential up to high scales (λ, λ_s > 0, |κ| < 8π, etc.).
    Used to cut the parameter space in Sec. II.A; standard for multi-scalar models.
  • domain assumption Freeze-out thermal production of the scalar DM (no freeze-in or non-thermal contributions).
    Explicitly stated in Sec. III; micrOMEGAs is run in freeze-out mode.
invented entities (2)
  • Real singlet scalar S (Z2-odd) as dark-matter candidate no independent evidence
    purpose: Provides the stable neutral particle whose relic density is computed.
    Standard singlet scalar DM; independent evidence would be a direct-detection or collider signal, neither of which exists yet.
  • Vector-like charged fermion doublet F_D and singlet E_S no independent evidence
    purpose: Mediate t/u-channel annihilation and co-annihilation; furnish the collider signature E1+E1- → e+e- + MET.
    New particles introduced by the model; their masses and couplings are free parameters. Collider projections supply a falsifiable handle, but no existing data confirm them.

pith-pipeline@v1.1.0-grok45 · 22942 in / 2881 out tokens · 26341 ms · 2026-07-12T00:01:47.030978+00:00 · methodology

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read the original abstract

We revisit a minimal fermion-portal scalar dark matter model consisting of a real singlet scalar dark matter candidate and additional vector-like singlet and doublet charged fermions stabilized by a discrete $Z_2$ symmetry. In light of the latest dark matter direct-detection constraints, the conventional Higgs-portal interaction is severely restricted, motivating a detailed investigation of fermion-mediated dark matter annihilation channels. We perform a comprehensive analysis of the model parameter space by incorporating theoretical constraints from vacuum stability and perturbative unitarity, together with experimental bounds from relic density measurements, direct-detection experiments, Higgs invisible decay searches, lepton-flavor-violating processes, and anomalous magnetic moments. We show that the observed dark matter relic abundance can be successfully reproduced over a wide mass range through Yukawa-driven $t$- and $u$-annihilation and co-annihilation processes involving the new fermions, while remaining consistent with current direct-detection limits. Motivated by the viable parameter space, we investigate the discovery prospects of the lightest charged vector-like fermion at future muon colliders operating at center-of-mass energies of 3 TeV and 10 TeV. Focusing on the process $\mu^+\mu^- \to E_1^+E_1^- \to e^+e^- + \cancel{E}_T$, we perform a detector-level analysis including realistic Standard Model backgrounds. We demonstrate that the clean experimental environment of a muon collider provides excellent sensitivity to charged fermion masses extending into the multi-TeV regime, significantly improving the exploration prospects of this class of fermion-portal dark matter scenarios.

Figures

Figures reproduced from arXiv: 2607.03775 by Madhurima Pandey, Najimuddin Khan, Songshaptak De, Tapoja Jha.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗

discussion (0)

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