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The paper argues that a Majorana singlet-doublet dark matter particle can match the observed relic density across a parameter range wider than previously thought for Dirac dark matter—with masses up to about 1750 GeV and mixings down to abo

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2026-08-03 21:34 UTC pith:ZHGQZ3X7

load-bearing objection Majorana SDDM conversion-driven scan extends the allowed relic parameter space, but internal inconsistencies and an unvalidated kinetic-equilibrium assumption keep the quantitative claim from being solid. the 4 major comments →

arxiv 2511.14571 v2 pith:ZHGQZ3X7 submitted 2025-11-18 hep-ph astro-ph.COhep-ex

Impact of conversion-driven processes on singlet-doublet Majorana dark matter relic

Partha Kumar Paul , Sujit Kumar Sahoo , Narendra Sahu This is my paper
classification hep-ph astro-ph.COhep-ex
keywords dark mattersinglet-doublet modelMajorana fermionthermal relicconversion-driven freeze-outco-scatteringrelic density
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.

This paper tries to establish that the singlet-doublet dark matter model with a Majorana fermion can produce the measured relic abundance over a much larger slice of parameter space than the Dirac version. Working within the thermal freeze-out framework, it argues that conversion-driven processes—decay, inverse decay, and co-scattering with standard-model particles—can deplete an otherwise overabundant singlet population even at very small mixing angles. If correct, the allowed region extends to dark matter masses around 1750 GeV and mixing angles as low as 2×10^-7, roughly twice the mass reach of the Dirac case. The paper also claims that including these processes shifts part of the viable parameter space into the sensitivity range of future collider and long-lived-particle experiments.

Core claim

The central claim is that in the Z2-odd singlet-doublet extension of the Standard Model, taking the dark matter to be a Majorana fermion—so that it is its own antiparticle—changes the relic-density calculation enough to open up a larger allowed region: 1 GeV ≲ M_DM ≲ 1750 GeV and 2×10^-7 ≲ sinθ ≲ 0.16 for mass splittings above 1 GeV. The authors solve two coupled Boltzmann equations, one for the singlet-like dark matter state and one for the heavier doublet states, with the conversion rate between the two sectors including both decay/inverse-decay and co-scattering off the SM bath. They find that for sinθ ≲ 0.05 the singlet decouples early with an excess abundance, and that conversion-driven

What carries the argument

The load-bearing object is the two-sector Boltzmann system, Eqs. (7)–(8), together with the conversion rate Γ2→1 = Γ2→1,0 + n_eq^SM ⟨σ_{2 0→1 0} v⟩. Sector 1 is the singlet-like dark matter; sector 2 is the remaining doublet states; sector 0 is the SM thermal bath. The conversion term couples the two dark-sector abundances, allowing the doublet, which stays in equilibrium through gauge interactions, to drain the early-decoupled singlet. The paper also defines ρ2 = Ω2s h^2 / Ω2s h^2(no co-scattering) to isolate the co-scattering contribution.

Load-bearing premise

The central assumption is that the dark sector can be split into exactly two internally-equilibrated sectors, with all conversion between them captured by a single rate (decay plus SM co-scattering); if that rate or the sector decomposition is wrong, the claimed allowed ranges shift.

What would settle it

A concrete falsifier would be a full numerical treatment that resolves the momentum distributions of the singlet and doublet states rather than assuming instantaneous internal equilibrium, or a computation of the neglected 1↔2 matrix elements; if the resulting relic density differs by more than the observed precision for benchmark points A–D, the two-sector approximation fails.

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

If this is right

  • For a Majorana singlet-doublet dark matter particle, the thermal-relic allowed mass range extends to M_DM ≈ 1750 GeV, more than twice the Dirac-model reach of ≈750 GeV.
  • Mixing angles as small as about 2×10^-7 remain compatible with the observed relic density, provided conversion-driven processes are included.
  • The combined direct-detection and collider bounds cap the mixing at sinθ ≲ 0.16, so the full allowed band lies below that.
  • In the small-mixing region sinθ ≲ 10^-5, co-scattering is essential: without it those points overproduce dark matter.
  • Conversion-driven processes push part of the allowed parameter space toward displaced-vertex signatures at colliders.

Where Pith is reading between the lines

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

  • The same two-sector treatment could be applied to other fermionic dark matter models where the dark matter candidate does not directly couple to the Standard Model, mapping out which models require conversion-driven depletion.
  • A concrete check of the paper's central approximation would be to compute the full set of 1↔2 scattering matrix elements and compare with the decay + SM co-scattering rate used here; if other channels are sizable, the small-sinθ boundary would shift.
  • If the Majorana hypothesis were confirmed, the enlarged parameter space would motivate searches for long-lived charged tracks, since small mixings imply longer decay lengths.
  • The ρ2 diagnostic could be reused as a public tool to quantify the importance of co-scattering in any two-sector freeze-out model.

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

4 major / 3 minor

Summary. The paper studies the singlet-doublet Majorana dark matter model and computes the thermal relic density using a two-sector Boltzmann treatment (Eqs. 7–8) that includes annihilation, co-annihilation, and conversion-driven processes (decay, inverse decay, and co-scattering). A numerical scan over M_DM, ΔM, and sinθ is performed, and the authors claim the correct relic density plus LZ/LEP constraints allow 1 GeV ≲ M_DM ≲ 1750 GeV and 2×10^-7 ≲ sinθ ≲ 0.16 for ΔM > 1 GeV. The abstract instead states 100 GeV ≲ M_DM ≲ 1750 GeV and sinθ ≲ 0.45. The paper argues this is a substantially larger parameter space than the Dirac case, and notes implications for displaced-vertex searches at LHC and MATHUSLA.

Significance. If the central claim is correct, the paper establishes that conversion-driven processes allow a much wider thermal-relic parameter space for Majorana singlet-doublet DM than previously recognized, including small sinθ down to ~10^-7 and masses up to ~1750 GeV. This would be of interest for dark matter model building and for collider searches of long-lived charged doublet partners. The paper introduces a useful quantitative diagnostic, ρ2, for the importance of co-scattering, and its displaced-vertex predictions are falsifiable. However, the quantitative claim is not yet fully supported: the two-sector Boltzmann equations rely on an unvalidated kinetic-equilibrium assumption in the small-sinθ regime, and several internal inconsistencies (abstract vs. body, scan range vs. quoted lower bound, an incorrect mixing-angle relation) undermine confidence in the reported ranges.

major comments (4)
  1. [Abstract and Sec. IV] The reported parameter ranges are internally inconsistent. The abstract states 100 GeV ≲ M_DM ≲ 1750 GeV and sinθ ≲ 0.45, while the conclusion (Sec. IV) states 1 GeV ≲ M_DM ≲ 1750 GeV and sinθ ≲ 0.16. The numerical scan is described in Sec. III as covering 10–2000 GeV, so the 1 GeV lower bound is not supported by the scan. These discrepancies change the claimed allowed region and must be reconciled; if the 1 GeV bound is inherited from earlier work, it should be stated as such, and the conclusion should reflect the actual scan range.
  2. [Eq. (5), Sec. II] The mixing-angle relation tan2θ = 2mD/(MΨ − Mχ3) is not consistent with the mass matrix (2) and the eigenvalues (4). For the two-state sub-block that mixes the singlet with the symmetric doublet combination, the standard relation involves the original diagonal mass parameter Mχ, not the eigenvalue Mχ3. As written, Eq. (5) is self-referential because Mχ3 itself depends on θ. Please correct or remove this equation. If it is used in the numerical scan, the results need to be re-examined; if it is not used, the model section should still present a correct relation.
  3. [Eqs. (7)–(8), Sec. III, BP2 in Table II] The two-sector Boltzmann equations assume that sector 1 (the DM) remains kinetically coupled to the SM bath, so that all thermally averaged cross sections and equilibrium abundances are evaluated at the SM temperature T. This is not justified in the small-sinθ regime that is central to the new results. For BP2 (M_DM = 972 GeV, sinθ = 7×10^-7, decoupling around z ~ 19), the DM–SM momentum-transfer rate is plausibly below the Hubble rate, so the DM may be kinetically decoupled. If so, the conversion-driven depletion is overestimated and the claimed lower bound sinθ ~ 2×10^-7, as well as the upward extension of M_DM to 1750 GeV, are not robust. Please provide a quantitative validation (e.g., compare elastic-scattering momentum-transfer rate with H) or adopt a treatment that accounts for a possible dark-sector temperature different from T.
  4. [Sec. III, Eq. (7)–(8) discussion] The rate Γ2→1 is defined only by the combination Γ2→1 = Γ2→1,0 + n_eq_SM ⟨σ2010 v⟩, but the paper gives no explicit expression for the decay width Γ2→1,0 or the co-scattering cross section σ2010. Since the new quantitative results depend sensitively on these rates, please provide the explicit definitions or a precise derivation/reference (e.g., to [34] or [38]) so that the calculation is reproducible. Without this, the central scan cannot be independently checked.
minor comments (3)
  1. [Abstract and Sec. I] Grammar: 'combinedly' should be 'combined' in the abstract; 'we assume the SDDM to be of Majorana type and studied' should be 'and study' in Sec. I.
  2. [Fig. 1 and Sec. III] The LEP bound is only referenced via [37]; the quantitative constraint (e.g., the mass limit on the charged doublet or the excluded ΔM region) is not stated. Please specify the actual LEP bound used.
  3. [Eq. (9)] The notation Ω_2s h^2 is confusing because it suggests the doublet (sector-2) relic, whereas it appears to denote the total dark-sector relic. Please rename or clarify the notation to avoid ambiguity.

Circularity Check

0 steps flagged

No significant circularity; the relic scan is constrained by external data and standard Boltzmann equations, with only a minor self-citation component.

full rationale

The central claim — that Majorana singlet-doublet DM with conversion-driven processes allows 1 GeV ≲ M_DM ≲ 1750 GeV and 2×10^-7 ≲ sinθ ≲ 0.16 — is obtained by numerically solving the coupled two-sector Boltzmann equations (7)-(8) and selecting parameter points that reproduce the external relic-density target Ωh^2 ≃ 0.12, then applying external LEP/LZ constraints. This is not a derivation that assumes its own conclusion. No fitted parameter is relabeled as a prediction: the relic density is the matched target, not an output used to define the inputs. Equation (5) is a diagonalization consistency relation, not a definition of the final relic result. The only self-referential element is that the Boltzmann equations are quoted from the authors' earlier Dirac paper [34] as well as the independent micrOMEGAs co-scattering study [38]; because the formalism is standard and externally supported, this self-citation is minor rather than load-bearing. The small-mixing extension depends on modeling assumptions — two-sector decomposition, sector-2 internal equilibrium, and kinetic coupling of the DM to the SM bath — and the paper also has internal inconsistencies (abstract upper bound sinθ≈0.45 versus body/conclusion 0.16; scan starting at 10 GeV versus quoted 1 GeV lower bound). These are correctness and robustness concerns, not circular reductions of the prediction to the input.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The central claim rests on a numerical scan over three model parameters (M_DM, ΔM, sinθ) plus a set of standard cosmological and dark-sector assumptions. No new particles or forces are introduced. The load-bearing assumptions are the two-sector Boltzmann decomposition and the specific conversion-rate composition; both are stated but not independently validated.

free parameters (3)
  • M_DM (Mχ3) = scanned 10-2000 GeV; quoted allowed 1-1750 GeV
    The DM mass is scanned and points selected by requiring Ωh²≈0.12; it is not predicted from first principles.
  • ΔM (Mχ1 - Mχ3) = scanned; quoted allowed ΔM>1 GeV
    Mass splitting controls co-annihilation, decay, and inverse-decay rates; it is varied to hit the relic target.
  • sinθ = scanned 2×10^-7 to 0.45 (abstract) / 0.16 (text); upper limited by LZ/LEP
    Mixing angle controls annihilation and direct detection; it is a scanned parameter, not a derived output.
axioms (6)
  • domain assumption Standard radiation-dominated cosmology with H = 1.66√g* T²/M_Pl and s = 2π²g* T³/45
    Used to convert Boltzmann equations into dY/dT form in Eq. (7); assumes standard thermal history.
  • domain assumption Two-sector coupled Boltzmann equations (7)-(8) fully describe dark-sector number densities
    Assumes sector 1 (DM) and sector 2 (heavier dark fermions) each evolve as single abundances and that internal kinetic equilibrium holds; not justified in detail.
  • domain assumption Conversion-driven rate Γ2→1 = Γ2→1,0 + n_eq_SM⟨σ2010 v⟩
    The only 2→1 conversion channels included are decay/inverse-decay and co-scattering with SM; other processes are neglected.
  • domain assumption The Z2-odd Lagrangian in Eq. (1) with singlet and doublet fermions is the complete dark sector
    No additional fields or couplings; the mass matrix and Yukawa relation Eq. (6) follow from this minimal setup.
  • domain assumption LZ direct-detection and LEP chargino bounds are correctly mapped onto the (M_DM, sinθ) plane
    Used to set the excluded regions in Figs. 3-4 and the quoted upper bound sinθ≲0.16; the recasting is not shown in the paper.
  • domain assumption Relic-density equality Ωh²≈0.12 is the selection criterion
    Points labeled 'correct relic' are fit to this external value; the tolerance or scan precision is not stated.

pith-pipeline@v1.3.0-alltime-deepseek · 9485 in / 15541 out tokens · 163257 ms · 2026-08-03T21:34:30.912229+00:00 · methodology

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read the original abstract

The singlet-doublet dark matter model offers a rich framework for exploring the nature of dark matter (DM) through its unique fermion structure. In this model, the important parameters are the singlet-doublet mass splitting $\Delta{M}$, the singlet-doublet mixing angle $\sin\theta$, and the DM mass $M_{\rm DM}$. If the DM is assumed to be of Dirac nature, then the annihilation, co-annihilation, and conversion driven processes combined allow a range of parameter space: $100~{\rm GeV} \lesssim M_{\rm DM}\lesssim750$ GeV and $10^{-6}\lesssim\sin\theta\lesssim0.04$ for $\Delta{M}>1$ GeV. While the nature of DM, either Dirac or Majorana, is not known, in this work, we assume the singlet-doublet DM to be of Majorana type and find that the relic density and direct detection can be satisfied over a larger parameter space. In particular, the allowed ranges of DM mass and $\sin\theta$ are $100~{\rm GeV}\lesssim M_{\rm DM}\lesssim1750$ GeV and $2\times10^{-7}\lesssim\sin\theta\lesssim0.45$ for $\Delta{M}>1$ GeV.

Figures

Figures reproduced from arXiv: 2511.14571 by Narendra Sahu, Partha Kumar Paul, Sujit Kumar Sahoo.

Figure 1
Figure 1. Figure 1: FIG. 1. [ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cosmological evolution of abundances of sector 1 and sector 2 particles for two sets of parameters illustrating co [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Correct dark matter relic points are shown in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Forward citations

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