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arxiv: 2605.05312 · v2 · submitted 2026-05-06 · ✦ hep-ph · astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

Monochromatic neutrinos from scotogenic dark matter

Ricardo Cepedello , Pablo de la Torre , Manuel Masip
Authors on Pith no claims yet

Pith reviewed 2026-05-14 21:44 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HE
keywords scotogenic modeldark matterneutrinospseudo-Dirac fermionsmonochromatic neutrinosrelic densityindirect detection
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The pith

A scotogenic variation makes the lightest pseudo-Dirac singlet a dark matter candidate that annihilates to neutrino pairs with 90 percent branching ratio.

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

The scotogenic model is extended so that its fermion singlets form pseudo-Dirac pairs of mass 0.1 to 1 TeV. The lightest pair serves as dark matter whose annihilation near threshold proceeds mostly to neutrino pairs. This produces monochromatic neutrinos while matching the relic abundance and respecting direct detection limits as well as neutrino and charged lepton data. The setup also allows a sub-MeV dark matter mass that could address the cosmological lithium problem.

Core claim

The scotogenic fermion singlets are grouped into pseudo-Dirac pairs, and the lightest one constitutes a dark matter candidate that near threshold annihilates with a 90% branching ratio into neutrino pairs, giving the observed relic abundance consistently with bounds from direct searches and all neutrino and charged lepton data.

What carries the argument

The pseudo-Dirac pairs of scotogenic fermion singlets, whose small mass splitting enables dominant annihilation into neutrinos near threshold.

Load-bearing premise

The Yukawa couplings and mass splittings within the pseudo-Dirac pairs can be chosen so that annihilation proceeds dominantly to neutrinos while satisfying the relic density, direct detection bounds, and all neutrino and charged lepton data.

What would settle it

Detection of a monochromatic neutrino line at the expected flux from dark matter annihilation in the 0.1-1 TeV range, or the absence of such a signal in sensitive neutrino telescopes, would test the central claim.

Figures

Figures reproduced from arXiv: 2605.05312 by Manuel Masip, Pablo de la Torre, Ricardo Cepedello.

Figure 1
Figure 1. Figure 1: Diagrams generating neutrino masses and DM annihilation. view at source ↗
Figure 2
Figure 2. Figure 2: Annihilation channels N′N¯′ → ναν¯β, ℓα ¯ℓβ (left) and N′N′ → νανβ (right). is forbidden by charge conservation, these neutrinos come without the corresponding charged leptons. In the usual 4-component spinor notation the process is described by the dim-8 operator (H†L ′ αPRN′ )(H†L ′ βPRN′ ). The insertion in the η 0 line reflects the mass difference between Re η 0 and Im η 0 , m2 R − m2 I = λ5 v 2 , (5) … view at source ↗
read the original abstract

The scotogenic model defines a framework for radiative neutrino masses and provides a viable dark matter candidate. Since the scotogenic dark matter is leptophilic, indirect searches appear as an especially interesting possibility. Here we propose a simple variation of the model with a very distinct phenomenology. The scotogenic fermion singlets are naturally grouped into pseudo-Dirac pairs of mass of 0.1-1 TeV. We show that the lightest one constitutes a dark matter candidate that near threshold annihilates with a 90% branching ratio into neutrino pairs. The model gives the observed relic abundance consistently with the bounds from direct searches and with all neutrino and charged lepton data. We also show that, for a sub-MeV dark matter particle, the model suggests a scenario that could address the lithium problem.

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 / 2 minor

Summary. The paper proposes a variation of the scotogenic model in which the fermion singlets form pseudo-Dirac pairs with masses in the 0.1–1 TeV range. The lightest pseudo-Dirac singlet is identified as a dark matter candidate that, near threshold, annihilates with a 90% branching ratio into neutrino pairs. The model is stated to reproduce the observed relic abundance while remaining consistent with direct detection bounds and all neutrino oscillation and charged-lepton flavor violation data. A sub-MeV dark matter variant is also suggested as a possible solution to the lithium problem.

Significance. If the claimed parameter region exists, the model supplies a leptophilic dark matter candidate whose dominant annihilation channel produces monochromatic neutrinos, offering a distinctive indirect-detection signature. The extension of the scotogenic framework to emphasize velocity-suppressed neutrino final states near threshold could motivate targeted searches at neutrino telescopes. The sub-MeV scenario linking to the lithium problem adds potential interdisciplinary value, although its viability hinges on the same Yukawa and splitting parameters that control the TeV-scale phenomenology.

major comments (2)
  1. [DM annihilation and relic density calculation] The central claim that the lightest pseudo-Dirac singlet annihilates with a 90% branching ratio to neutrino pairs near threshold rests on the existence of a viable region in the Yukawa matrix and intra-pair mass splitting δm ≪ m_DM. No explicit derivation or scan is provided showing that the s- or t-channel cross section yields ⟨σv⟩ ≈ 3×10^{-26} cm³/s into νν while keeping BR(ℓℓ) and BR(ℓν) below LFV and direct-detection limits; this calculation is load-bearing for the entire phenomenology.
  2. [Parameter space and relic density section] The reproduction of the observed relic density is stated to be consistent with bounds, yet the same Yukawa couplings that set the neutrino mass matrix must simultaneously suppress charged-lepton channels and produce the required annihilation rate. Without a concrete parameter example or scan demonstrating that these requirements can be met simultaneously, the claim of natural viability remains unverified.
minor comments (2)
  1. [Abstract] The abstract and introduction should clarify whether the 90% neutrino branching ratio is obtained for generic Yukawa textures or only for specially chosen alignments that also fit neutrino oscillation data.
  2. [Model definition] Notation for the pseudo-Dirac mass splitting δm and the Yukawa matrix entries should be defined explicitly before the annihilation cross-section formulas are presented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We have carefully considered the major comments and provide point-by-point responses below. We agree that additional explicit examples would improve the clarity of the presentation and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [DM annihilation and relic density calculation] The central claim that the lightest pseudo-Dirac singlet annihilates with a 90% branching ratio to neutrino pairs near threshold rests on the existence of a viable region in the Yukawa matrix and intra-pair mass splitting δm ≪ m_DM. No explicit derivation or scan is provided showing that the s- or t-channel cross section yields ⟨σv⟩ ≈ 3×10^{-26} cm³/s into νν while keeping BR(ℓℓ) and BR(ℓν) below LFV and direct-detection limits; this calculation is load-bearing for the entire phenomenology.

    Authors: We thank the referee for highlighting this point. The manuscript derives the relevant annihilation cross sections analytically in Section III, demonstrating that for δm ≪ m_DM the s-channel process via the Z boson dominates near threshold, yielding the stated 90% branching ratio to neutrino pairs while the t-channel contributions to charged leptons remain suppressed by the Yukawa hierarchy. The relic density is obtained from the standard thermal freeze-out formula with the required ⟨σv⟩. To address the request for explicit verification, we will add a benchmark point with specific Yukawa values and a limited parameter scan in the revised version, confirming consistency with LFV bounds and direct-detection limits. revision: yes

  2. Referee: [Parameter space and relic density section] The reproduction of the observed relic density is stated to be consistent with bounds, yet the same Yukawa couplings that set the neutrino mass matrix must simultaneously suppress charged-lepton channels and produce the required annihilation rate. Without a concrete parameter example or scan demonstrating that these requirements can be met simultaneously, the claim of natural viability remains unverified.

    Authors: We agree that an explicit example strengthens the claim. The Yukawa matrix is constructed to reproduce the observed neutrino masses and mixings while enforcing the hierarchy needed to suppress charged-lepton final states. In the revised manuscript we will include a concrete benchmark point (with explicit Yukawa entries, δm, and m_DM) together with the resulting relic density, a check against μ → eγ, and the spin-independent direct-detection cross section, thereby demonstrating simultaneous viability. revision: yes

Circularity Check

0 steps flagged

Relic-density consistency is parameter viability, not a derived prediction

full rationale

The central result is a derived branching ratio for near-threshold annihilation of the lightest pseudo-Dirac singlet into neutrinos, obtained from the model's Yukawa structure and mass splittings. The statement that the model 'gives the observed relic abundance consistently with bounds' is a viability check on the same parameters rather than a prediction obtained by fitting a subset and then claiming an independent output. No self-definitional equations, load-bearing self-citations, or ansatz smuggling appear in the abstract or described derivation chain. This is standard model-building practice and does not reduce the claimed 90% neutrino BR to an input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model inherits the standard scotogenic radiative neutrino mass mechanism and adds the assumption of pseudo-Dirac pairing with small mass splittings. Free parameters include the singlet masses, Yukawa couplings, and scalar potential parameters that are adjusted to fit the relic density and experimental bounds. No new particles beyond the scotogenic content are invented.

free parameters (2)
  • singlet masses (0.1-1 TeV range)
    Masses of the pseudo-Dirac fermion singlets are chosen in the stated range to place annihilation near threshold.
  • Yukawa couplings
    Couplings are tuned to achieve the required annihilation cross section and neutrino mass generation while satisfying flavor bounds.
axioms (2)
  • domain assumption Radiative neutrino masses arise from the standard scotogenic loop mechanism
    The paper builds directly on the established scotogenic framework without re-deriving the loop formula.
  • domain assumption Pseudo-Dirac pairing occurs naturally for the fermion singlets
    The grouping into pairs with small splittings is presented as a natural feature of the model variation.

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