MeV neutrino dark matter: Relic density, lepton flavour violation and electron recoil

C. Weinheimer; J. Fiaschi; M. Klasen; M. Vargas; S. Zeinstra

REVIEW 2 major objections 4 minor 1 cited by

MeV neutrino dark matter: Relic density, lepton flavour violation and electron recoil

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper shows that MeV-to-GeV right-handed neutrino dark matter in the SLIM model can reproduce the observed relic density and neutrino masses, but lepton-flavour-violation limits from MEG and SINDRUM push the electron-recoil cross…

desk verdict Useful, mostly sound constraints study for MeV neutrino DM, but the MEG-based electron-recoil bound is only proven for a real Casas-Ibarra angle, so the headline needs a caveat or a complex-angle rerun. read the letter →

arxiv 1908.09882 v2 pith:KEGG325Q submitted 2019-08-26 hep-ph hep-ex

J. Fiaschi , M. Klasen , M. Vargas , C. Weinheimer , S. Zeinstra This is my paper · ORCID

classification hep-phhep-ex

keywords darkmatterright-handedneutrinoSLIMmodelleptonflavourviolationmutoegammaelectronrecoilrelicdensityCasas-Ibarraparametrization

topics Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether right-handed neutrinos with masses of a few MeV to a few GeV can be the dark matter, in a minimal extension of the Standard Model called the SLIM model, where one scalar singlet and one scalar doublet generate neutrino masses in a loop. It finds that matching the observed dark-matter relic density and the measured neutrino mass differences and mixings forces the dark matter's couplings to charged leptons to be sizeable, between a few $10^{-4}$ and a few $10^{-1}$. Those same couplings inevitably generate lepton-flavour-violating processes such as $\mu\to e\gamma$, and the current MEG limit already rules out couplings above about $6\times 10^{-3}$. As a result, the DM-electron recoil cross section reaches at most a few $10^{-46}\,\mathrm{cm}^2$ under all low-energy, collider, cosmological and neutrino constraints, and drops to at most $10^{-52}\,\mathrm{cm}^2$ once lepton-flavour-violation limits are imposed—far below the realistic sensitivity of XENON1T. The broader point is that lepton-flavour violation, rather than direct detection, is the bottleneck that decides whether this class of MeV neutrino dark-matter models survives.

What carries the argument

The load-bearing machinery is the radiative-seesaw connection between neutrino masses and dark-sector couplings. The active neutrino mass matrix is a one-loop sum over the two right-handed neutrinos and the real and imaginary neutral scalars, Eq. (3.4), controlled by the small mass splitting $m_4$; inverting this matrix with the Casas-Ibarra parametrization—a standard inversion that converts measured neutrino masses and mixings into the Yukawa couplings of a radiative seesaw—gives $\lambda_8 = M^{-1/2} R D_\nu^{1/2} U_\nu^\dagger$, Eq. (3.11), so the same coupling matrix drives relic density, LFV and direct detection. The cross-section side is carried by the non-relativistic electron-recoil formula $\bar\sigma_{\chi e}=\mu_{\chi e}^2(\lambda_8^{e1})^4/(\pi m_{\eta^\pm}^4)$, where the charged scalar mass is bounded by LEP at 98.5 GeV; because this mass enters to the fourth power, the predicted signals are strongly suppressed even when the couplings are large.

What would settle it

A decisive test would be to rerun the full parameter scan with the Casas-Ibarra inversion for a massive lightest active neutrino and for the inverted neutrino ordering. If any point reproduces the observed relic density and neutrino data, passes the LEP and cosmological constraints, and has $|\lambda_8^{e1}|>6\times 10^{-3}$ (or an electron-recoil cross section above $10^{-52}\,\mathrm{cm}^2$) while respecting the MEG, SINDRUM and SINDRUM II bounds, the paper's central exclusion would be contradicted. On the experimental side, the MEG upgrade to $2\times 10^{-15}$ on $\mathrm{BR}(\mu\to e\gamma)$ is the sharpest near-term test: a positive signal would need to be accompanied by the correlated $\mu\to 3e$ and $\mu\to e$ conversion rates predicted here, while a null result would close most of the remaining window.

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Extended reading notes

Core claim

The paper's central finding is that in the SLIM model with right-handed neutrino DM, the same Yukawa matrix $\lambda_8$ that generates the observed active neutrino masses at one loop also sets the relic abundance, the lepton-flavour-violating rates, and the electron-recoil cross section. The one-loop neutrino mass matrix of Eq. (3.4) is inverted with the Casas-Ibarra parametrization, taking a massless lightest active neutrino and normal ordering, so that the measured PMNS mixing and mass splittings fix $\lambda_8$ up to the dark-sector masses, the mixing angles, and one free angle $\theta$. Scanning over these parameters while imposing the observed relic density and the LEP, LHC and cosmological constraints, the viable models have DM masses above a few MeV (consistent with BBN) and DM-lepton couplings between a few $10^{-4}$ and a few $10^{-1}$. Those couplings make $\mu\to e\gamma$, $\mu\to 3e$, and $\mu\to e$ conversion in titanium unavoidable: neutrino masses alone force $\mathrm{BR}(\mu\to e\gamma)$ above about $10^{-17}$, the MEG bound of $4.2\times 10^{-13}$ excludes $|\lambda_8^{e1}|>6\times 10^{-3}$, and the planned MEG upgrade at $2\times 10^{-15}$ would test almost all of the remaining parameter space. For electron recoil the charged scalar mediator enters as $\bar\sigma_{\chi e}=\mu_{\chi e}^2(\lambda_8^{e1})^4/(\pi m_{\eta^\pm}^4)$; with the LEP limit $m_{\eta^\pm}>98.5$ GeV, the largest allowed couplings give at most a few $10^{-46}$ cm$^2$, and after the LFV limits at most $10^{-52}$ cm$^2$.

Load-bearing premise

The load-bearing assumption is that the lightest active neutrino is massless and the neutrino masses follow the normal ordering; if the lightest neutrino has a non-zero mass or the ordering is inverted, the Casas-Ibarra inversion produces different couplings $\lambda_8$, and the quoted lepton-flavour-violation and electron-recoil limits would have to be recomputed.

Editorial extensions

If this is right

If the SLIM model with right-handed neutrino dark matter is correct, MEG's current limit already excludes DM-electron couplings above about $6\times 10^{-3}$, and the upgraded MEG experiment at $2\times 10^{-15}$ will probe nearly all of the remaining parameter space.
The predicted electron-recoil cross sections, at most $10^{-52}\,\mathrm{cm}^2$ after lepton-flavour-violation limits, lie far outside the reach of current and near-future liquid-xenon detectors, including the S2-only XENON1T analysis.
Viable dark-matter masses in the scan automatically sit above a few MeV, so the model is consistent with big-bang nucleosynthesis bounds without extra cosmological tuning.
The three lepton-flavour-violating channels $\mu\to e\gamma$, $\mu\to 3e$ and $\mu\to e$ conversion are strongly correlated, so a discovery in one channel predicts a narrow range of rates in the other two.
Because the suppression comes from the fourth power of the charged scalar mass, any observable electron-recoil signal would require a mediator lighter than the LEP bound, which this minimal model does not allow.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's bounds are conditional on the chosen neutrino sector; testing an inverted mass ordering or a non-zero lightest neutrino mass is the natural next calculation, and could shift the $\lambda_8$ values and the derived cross-section ceilings.
The charged-scalar-mass suppression mechanism is not specific to SLIM: any MeV-to-GeV neutrino dark-matter model with a charged scalar mediator above the LEP bound will inherit the same fourth-power suppression, so the qualitative no-detectable-electron-recoil conclusion should extend to similar radiative-seesaw constructions.
If MEG's upgrade observes $\mu\to e\gamma$, the rate alone will not identify the model; the decisive cross-check is whether $\mu\to 3e$ and $\mu\to e$ conversion in titanium appear at the correlated rates shown in the paper, which would distinguish this scenario from other sources of lepton flavour violation.
Reaching this model class experimentally would seem to require either sub-keV detectors with large exposure or a way to evade the LEP bound on the charged scalar, neither of which is present in the minimal setup studied here.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a competent constraints paper for MeV-scale right-handed neutrino DM in the SLIM/scotogenic framework. The genuinely new content is the numerical relic-density scan with Casas-Ibarra neutrino constraints and the first LFV analysis (mu->e gamma, mu->3e, mu-e conversion) for this model. The main quantitative result is that MEG already cuts the lambda_e1 coupling above a few 10^-3 and, if applied, pushes the electron-recoil cross section below 10^-52 cm^2. The paper also does a careful job on XENON sensitivities; the conclusion that this model is invisible to electron recoil is robust because it is driven by the LEP bound m_eta+ > 98.5 GeV, which enters to the fourth power.

Credit where due: the authors use public codes (SARAH/SPheno/micrOMEGAs), the scan is described well enough to reproduce, and the LFV plots are physically sensible because neutrino masses force a lower floor on lambda8. The abstract's BBN sentence is stronger than what the scan actually shows--most viable models have m_N1 above a few MeV, but the scan allowed lower masses--and no scan code or data files were released. Those are minor.

The real soft spot is the one the stress test flags. In Sec. 3.3 the Casas-Ibarra rotation is taken real (Eq. 3.9). With two right-handed neutrinos, the general solution of Eq. (3.8) allows a complex 2x2 orthogonal block, and that complex phase can make the mu->e gamma amplitude vanish by cancellation between the N1 and N2 loop contributions. The claimed MEG bound and the resulting sigma_e <= 10^-52 cm^2 are therefore only established on a real-theta slice, not over the full lambda8 parameter space. This does not kill the paper's main point: because the charged scalar is heavy, electron recoil stays far below current and planned sensitivities even at the 10^-46 cm^2 level. But the headline "MEG excludes these couplings" is conditional, and the paper should either extend the scan to complex R or explicitly state the restriction.

The neutrino-mass assumption (normal hierarchy, massless lightest neutrino) is also a simplification and is not tested; it is standard, so I would call that a minor caveat rather than a flaw.

For whom: phenomenologists working on sub-GeV DM or LFV in radiative seesaw models will get value here, and the XENON sensitivity discussion is useful reference material. It deserves a serious referee. I would send it to review with a request to address the complex-Casas-Ibarra issue before publication, but I would not desk-reject it. My recommendation: engage with it, ask for a clarification or a rerun with complex R, and if that cannot be done, ask them to soften the MEG-based claim accordingly.

Referee Report

2 major / 4 minor

Summary. The paper studies a scotogenic/SLIM extension of the Standard Model containing two right-handed Majorana neutrinos (a light DM candidate N1 and a heavier N2) plus a complex scalar doublet and singlet. It imposes collider, cosmological and neutrino mass/mixing constraints, uses the Casas-Ibarra parametrization to fix the Yukawa couplings λ8, computes the DM relic density with micrOMEGAs, and then studies one-loop lepton flavour violation (μ→eγ, μ→3e, μ-Ti→e-Ti) and the DM-electron recoil cross section for XENON1T and near-future detectors. The central quantitative claims are that the correct relic density forces sizeable couplings to charged leptons, that MEG already excludes |λ_e1| larger than about 6×10^-3, that lepton flavour violation reduces the electron recoil cross section to at most about 10^-52 cm^2 (with at most about 10^-46 cm^2 even before LFV constraints), and that the model is therefore unobservable in current and near-future electron-recoil searches.

Significance. If the central claims hold, this is a useful and falsifiable study: it closes a gap in the SLIM literature by imposing the Planck relic density and neutrino mixing data simultaneously, and it identifies lepton flavour violation as a much stronger constraint than previously appreciated. The detailed XENON1T sensitivity estimate, including the S2-only analysis and realistic threshold/background assumptions, is also a valuable comparison for the sub-GeV dark matter community. Strengths of the paper are its use of public numerical tools (SARAH, SPheno, micrOMEGAs), the explicit parameter ranges in Table 1, and the honest evaluation of irreducible backgrounds and energy thresholds. The qualitative conclusion that the electron recoil signal is far below experimental reach is robust to the issue raised below; the quantitative LFV exclusion is not yet demonstrated over the full model parameter space.

major comments (2)

[Sec. 3.3, Eq. (3.9)] The parametrization is restricted to a real orthogonal matrix R with θ ∈ [0, 2π]. For two right-handed neutrinos and one massless active neutrino, the general solution of Eq. (3.8) is a complex 2×3 matrix (equivalently a complex 2×2 rotation in the non-zero block); the complex angle changes the magnitudes and relative phases of the entries of λ8 without changing the light-neutrino mass matrix. Since the μ→eγ amplitude in Sec. 5 is A = Σ_i λ_ei λ_μi^* f(m_Ni^2/m_η^2), and f(m_N1^2) differs from f(m_N2^2), the two terms can interfere destructively for a complex R, so |λ_e1| can be O(0.1) with BR(μ→eγ) below the MEG bound. The statements that MEG excludes λ_e1 > 6×10^-3 and that LFV limits the electron recoil cross section to at most 10^-52 cm^2 are therefore not demonstrated on the full parameter space. Please extend the scan to a complex Casas-Ibarra angle, or prove that cancellations cannot occur, and re-derive the LFV and recoil limits accordingly.
[Sec. 3.3, Eq. (3.5)] Only the normal hierarchy with m_1 = 0 is implemented, and this restriction is stated as an assumption 'for simplicity'. An inverted hierarchy with m_3 = 0 is also compatible with two right-handed neutrinos and would generically produce different λ8 matrices, different LFV rates, and different electron-recoil cross sections. Since the paper repeatedly refers to a comprehensive scan and to upper bounds on the recoil cross section, the authors should either include the inverted-hierarchy case or explicitly restrict the exclusion statements and the 10^-52 cm^2 bound to the normal hierarchy.

minor comments (4)

[Sec. 3.3, Eq. (3.6)] The text says that M is a 3×3 diagonal matrix, but with λ8 a 2×3 matrix the sum over the two right-handed neutrinos in Eq. (3.4) requires a 2×2 diagonal matrix; please correct the dimension or clarify the notation.
[Sec. 4] There is a typo in the sentence describing the b→sγ constraint: 'braching ratio' should be 'branching ratio'.
[Sec. 5] The statement that non-zero neutrino masses impose a lower bound BR(μ→eγ) ≳ 10^-17 should specify whether this is a hard bound over all scanned points or only a feature of the real-θ slice shown in Fig. 5; as written it reads like a general theorem.
[Sec. 6.2 and Fig. 9] The idealized red dotted sensitivity curve is scaled by exposure only, and the text correctly notes that this neglects the irreducible neutrino background; please state explicitly in the caption that this curve is an idealized projection rather than a limit, and consider separating projected sensitivities from published limits to improve legibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SLIM model predictions are derived from independent inputs and external constraints; self-citations are not load-bearing.

full rationale

The derivation chain is self-contained. The Lagrangian (Eq. 2.3) defines the model with free couplings; the one-loop neutrino mass formula (Eq. 3.4, from previous work) together with the Casas-Ibarra parametrization (Eqs. 3.5-3.11) inverts the neutrino data to determine λ8. The relic density is then computed numerically (Sec. 4) and the Planck band is imposed as a constraint; the LFV rates (Sec. 5) and electron recoil cross section (Eqs. 6.8-6.10) are computed from the resulting λ8 and masses and compared with external MEG, SINDRUM, LEP and XENON1T bounds. None of the headline results — the lower bound BR(μ→eγ) ≈ 10^-17, the exclusion of |λ8^{e1}| > 6×10^-3, or σ̄ ≤ 10^-52 cm² — is used as an input in constructing λ8 or in selecting the scan points; they are outputs of the scan after imposing neutrino, relic-density, collider and cosmological constraints. The self-citations (e.g., Refs. [23, 25] for the model, and Refs. [4, 14, 19, 71] for related phenomenology) define the model or cite prior calculations but do not replace an independent derivation of the new LFV and electron-recoil results. The restriction to a real Casas-Ibarra angle θ and a massless lightest neutrino discussed in Sec. 3.3 is a limitation on parameter-space coverage, not a circular reduction: it affects whether the quoted bounds cover the full model space, not whether they are derived from the inputs by construction. Therefore the paper does not exhibit circular reasoning.

Assumptions & free parameters 8 free parameters · 6 assumptions · 4 invented entities

The central claims rest on the assumed SLIM model particle content and the one-loop neutrino mass formula, together with a set of hand-chosen scan parameters. The LFV and electron recoil conclusions are conditional on the Casas-Ibarra parametrization being representative of the full neutrino sector. No new particles are introduced beyond those already in the cited model.

free parameters (8)

m4 = 10 keV to 10 MeV (scanned)
Soft U(1) breaking mass, controls scalar mass splitting and the neutrino mass loop; scanned range from Sec. 3.2.
epsilon = 10^-5 to 6.1e1 GeV^2 (scanned)
Mass-splitting parameter in Eq. (2.8); small values produce MeV-scale light scalars needed for the structure formation solution.
m_N1 = 0.1 to 0.98 times m_zeta2 (scanned)
DM mass; the upper end near m_zeta2 keeps the DM slightly lighter than the lightest scalar as required by Refs [34,35].
m_N2 = 10 to 200 GeV (scanned)
Heavy sterile neutrino that generates neutrino masses and decays promptly; mass range from Sec. 3.2.
theta (Casas-Ibarra angle) = 0 to 2 pi (scanned)
Free angle in the Casas-Ibarra parametrization, Eq. (3.9), determines the flavour structure of lambda8.
lambda4 = 0.097
Fixed by hand to satisfy the LEP limit on m_eta+ and R_gamma_gamma (Sec. 3.1).
lambda5 = 0.13
Fixed alongside lambda4 to satisfy the same constraints (Sec. 3.1).
lambda6 = 2.3
Set to produce MeV scalar masses; varied indirectly through epsilon (Sec. 3.2).

assumptions (6)

domain assumption The SLIM scalar sector with complex singlet rho and complex doublet eta, and the Lagrangian in Eq. (2.3), is the correct low-energy effective theory.
The entire analysis is performed within this model from Refs [22,23,25]; the paper provides no independent evidence for these fields.
domain assumption Two right-handed Majorana neutrinos N1 and N2 exist with masses in the scanned ranges.
Required for radiative neutrino masses and dark matter; assumed from the model.
domain assumption The one-loop active neutrino mass formula of Eq. (3.4) from Ref [25] is correct.
All derived couplings lambda8 and subsequent LFV and direct detection predictions depend on this formula.
domain assumption Normal neutrino mass hierarchy with massless lightest active neutrino.
Adopted in Sec. 3.3 to simplify the Casas-Ibarra parametrization; inverted hierarchy or nonzero m1 would alter lambda8 and the constraints.
domain assumption The structure formation constraints of Refs [34,35] apply, requiring a small mass splitting between N1 and the lightest scalar.
Used in Sec. 3.2 to set the scan ranges; if these constraints are relaxed, the allowed parameter space changes.
domain assumption The LEP limit m_eta+/- > 98.5 GeV applies to the charged scalar in this model.
Sets m_eta+/- around 99 GeV in Eq. (2.4) and strongly suppresses electron recoil and LFV rates.

invented entities (4)

Right-handed Majorana neutrino N1
purpose: Dark matter candidate in the MeV to GeV mass range.
Postulated by the SLIM model; this paper only derives constraints on its couplings and mass, with no direct experimental handle.
Right-handed Majorana neutrino N2
purpose: Generates the two non-zero active neutrino masses at one loop and decays promptly.
Model input; no independent evidence presented.
Complex scalar singlet rho
purpose: Mixes with the doublet to produce a MeV-scale light scalar zeta2, enabling the DM mass below the scalar mass as needed for structure formation.
Taken from Refs [22,23,25].
Complex scalar doublet eta
purpose: Its charged component mediates DM annihilation, lepton flavour violation, and electron scattering.
Model input; the charged component is constrained by LEP, which is the main handle but not evidence of the particle's existence.

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Cite this review

Pith. "Pith review of MeV neutrino dark matter: Relic density, lepton flavour violation and electron recoil." pith.science (2026). https://pith.science/paper/KEGG325Q

@misc{pith2026190809882,
  author       = {Pith},
  title        = {Pith review of: MeV neutrino dark matter: Relic density, lepton flavour violation and electron recoil},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KEGG325Q}},
  note         = {Machine review of arXiv:1908.09882}
}

read the original abstract

Right-handed neutrinos with MeV to GeV mass are very promising candidates for dark matter (DM). Not only can they solve the missing satellite puzzle, the cusp-core problem of inner DM density profiles, and the too-big-to fail problem, {\it i.e.} that the unobserved satellites are too big to not have visible stars, but they can also account for the Standard Model (SM) neutrino masses at one loop. We perform a comprehensive study of the right-handed neutrino parameter space and impose the correct observed relic density and SM neutrino mass differences and mixings. We find that the DM masses are in agreement with bounds from big-bang nucleosynthesis, but that these constraints induce sizeable DM couplings to the charged SM leptons. We then point out that previously overlooked limits from current and future lepton flavour violation experiments such as MEG and SINDRUM heavily constrain the allowed parameter space. Since the DM is leptophilic, we also investigate electron recoil as a possible direct detection signal, in particular in the XENON1T experiment. We find that despite the large coupling and low backgrounds, the energy thresholds are still too high and the predicted cross sections too low due to the heavy charged mediator, whose mass is constrained by LEP limits.

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