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Bounds and detection of MeV-scale dark matter annihilation to neutrinos

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Relic dark matter annihilation after neutrino decoupling adds a nonthermal neutrino energy density that strengthens cosmological bounds on the annihilation cross section, making them competitive with neutrino detector limits in some…

desk verdict The nonthermal Neff constraints exceed the available DM rest energy by orders of magnitude; the thermal dataset update is fine, but the new cross-section bounds are not self-consistent. read the letter →

arxiv 2506.04568 v2 pith:M625V3EF submitted 2025-06-05 hep-ph hep-ex

Shinya Kanemura , Shao-Ping Li , Dibyendu Nanda This is my paper
classification hep-phhep-ex
keywords darkmatterannihilationMeV-scaleneutrinodecouplingeffectivenumberofneutrinosnonthermalreliccosmologicalconstraintsdetectors
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 argues that MeV-scale dark matter annihilating into neutrinos with a cross section above the standard thermal freeze-out value leaves two imprints on the cosmic neutrino background: entropy injection while neutrinos are still in thermal contact, which raises the effective number of neutrino species $N_{\rm eff}$, and nonthermal neutrino energy released by the surviving relic population after decoupling, which also adds to $N_{\rm eff}$. Combining both effects yields upper bounds on the annihilation cross section $\langle\sigma v\rangle$ that in some mass ranges are comparable to or stronger than the limits from neutrino telescopes. The paper also shows that the lower mass bounds derived from $N_{\rm eff}$ are dataset-dependent, ranging from about 3 MeV to 13 MeV for a real scalar dark matter candidate depending on which cosmological data are used. If correct, this determines how much parameter space upcoming neutrino detectors can actually probe.

What carries the argument

The argument is carried by the two-stage treatment of dark matter annihilation into neutrinos. During neutrino decoupling, the dark matter is taken to remain in thermal contact with neutrinos, and its entropy injection is tracked with coupled Boltzmann equations for the neutrino and photon temperatures $T_\nu$ and $T_\gamma$, following the approach of Ref. [29]; this yields the thermal contribution $N_{\rm eff}^{\rm th}$. After decoupling is complete, the relic number density is assumed to redshift as $n_{\rm DM}=n_{\rm DM,0}(a_0/a)^3$, and the nonthermal energy release is governed by the evolution equation $\mathrm{d}Y_\nu/\mathrm{d}T = -2C_\nu/(s_{\rm SM}^{4/3}HT)$ with collision rate $C_\nu=\langle\sigma v\rangle m_{\rm DM}n_{\rm DM}^2$, producing $N_{\rm eff}^{\rm nth}$. The key identity is the sum $N_{\rm eff}=N_{\rm eff}^{\rm th}+N_{\rm eff}^{\rm nth}$, whose logarithmic growth makes late-time annihilation relevant all the way down to recombination.

What would settle it

A CMB experiment measuring $N_{\rm eff}=3.04\pm0.02$ with no dark-matter excess would falsify the paper's prediction of $\Delta N_{\rm eff}\simeq0.08$ for a 3 MeV real scalar with $\langle\sigma v\rangle=10^{-23}\,{\rm cm^3\,s^{-1}}$; because the paper claims cosmological constraints are competitive precisely in this regime, such a null result would close the window where relic annihilation rivals neutrino detectors.

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Extended reading notes

Core claim

The central claim is that relic dark matter annihilation after neutrino decoupling, previously ignored in MeV-scale constraints, contributes a non-negligible nonthermal neutrino energy density that strengthens the cosmological bound on the annihilation cross section. The paper derives the closed-form estimate $N_{\rm eff}^{\rm nth}\simeq0.002\,(\langle\sigma v\rangle/10^{-24}\,{\rm cm^3\,s^{-1}})(1\,{\rm MeV}/m_{\rm DM})\ln(T_{\rm dec}/T_{\rm CMB})$, with the logarithm around 12, so a suppressed late-time annihilation rate still produces a percent-level shift in $N_{\rm eff}$. Adding this to the thermal entropy-injection contribution, the authors find that the combined $N_{\rm eff}$ constraint excludes cross sections in the range accessible to current and near-future neutrino detectors, and in the low-mass regime the cosmological bound becomes stronger than the detector limits. On the mass side, the lower bounds are dataset-dependent: for a real scalar with one internal degree of freedom, the bound varies from about 3 MeV with the most permissive recent data to 13.3 MeV with the tightest, so the authors conclude that a definitive lower limit is not yet established.

Load-bearing premise

The bounds assume the dark matter number density at any early time equals the present-day relic density scaled back by cosmic expansion, meaning dark matter was fully produced before the end of neutrino decoupling and is not significantly depleted by the annihilation being constrained.

Editorial extensions

If this is right

  • In the low-mass regime (a few MeV), the cosmological constraint on $\langle\sigma v\rangle$ from the nonthermal contribution becomes stronger than the current limits from neutrino detectors.
  • The parameter space that future neutrino detectors can target depends critically on the $\Delta N_{\rm eff}\simeq0.2$–$0.4$ window favoured by attempts to relieve the Hubble tension; upcoming neutrino experiments are expected to cover that window for a real scalar dark matter particle.
  • Because the nonthermal contribution scales with $\langle\sigma v\rangle/m_{\rm DM}$ and grows logarithmically with the ratio of decoupling to recombination temperature, it cannot be neglected even when the late-time annihilation rate appears small.
  • With the most permissive recent dataset, a real scalar dark matter mass as low as 3 MeV remains allowed, while the tightest dataset pushes the bound to 13.3 MeV, leaving the lower mass limit inconclusive.

Reading between the lines

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

  • We infer that the nonthermal neutrino spectrum from relic annihilation is roughly mono-energetic at $E_\nu \simeq m_{\rm DM}$; a full momentum-dependent transport calculation could predict a spectral feature in future cosmic-neutrino experiments, not just a shift in $N_{\rm eff}$.
  • We infer the same two-stage treatment applies to dark matter annihilating into other invisible final states, such as sterile neutrinos, where the nonthermal energy release would contribute to $N_{\rm eff}$ and the bounds would depend on the final-state spectrum.
  • We infer that if the dark matter relic density is produced by freeze-in or another mechanism unfinished at decoupling, the $n_{\rm DM}$ scaling in the paper overestimates the late-time collision rate, so the bounds should be rescaled by the actual production history.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper considers MeV-scale dark matter that annihilates into neutrinos with cross sections larger than the standard thermal freeze-out value, motivated by non-standard production mechanisms such as super-WIMP late-time decay. The authors combine two cosmological effects: (i) entropy injection during neutrino decoupling, which modifies the neutrino-to-photon temperature ratio and raises Neff, and (ii) nonthermal neutrino energy release from relic DM annihilation after decoupling, which they compute by integrating the annihilation rate with a DM number density fixed to the present-day value scaled back in time. Using recent Neff measurements from Planck, DESI, ACT, and SPT-3G, they derive lower bounds on the DM mass and upper limits on the annihilation cross section, claiming that in some mass regimes the latter are competitive with or stronger than current neutrino-detector bounds. They also discuss the implications for JUNO and the parameter space that would yield ΔNeff = 0.2–0.4.

Significance. If the nonthermal-Neff calculation were correct, the paper would introduce a genuinely new cosmological probe of DM annihilation to neutrinos that could exceed the sensitivity of neutrino telescopes, and it would demonstrate that the lower mass bound is strongly dataset-dependent. The dataset dependence of the thermal (entropy-injection) bound is a valid and timely observation, and the paper usefully surveys the latest Neff measurements. The analytic machinery for the thermal part is transparent and follows established work (Escudero 2019; Sabti et al. 2020). However, the central new ingredient—the post-decoupling relic-annihilation contribution, Eqs. (11)–(16)—is not self-consistent because it ignores the depletion of the DM population. The resulting N_nth values exceed the available DM rest energy by large factors in precisely the parameter regions where the claimed constraints are competitive. This invalidates the paper's main quantitative claims, so the positive aspects of the paper do not outweigh the load-bearing error.

major comments (2)
  1. [Section II, Eqs. (11)-(16), Figs. 1-2] The nonthermal Neff calculation is not self-consistent because Eq. (13) is integrated with nDM held fixed at the present-day value scaled back, Eqs. (22)-(23), while the annihilation itself is neglected in the evolution of nDM. For the cross sections that produce non-negligible N_nth, the annihilation rate at T_dec = 10 keV is Γ/H = nDM⟨σv⟩/H ≈ 3.4 for m = 1 MeV, ⟨σv⟩ = 10^-24 cm^3/s, and ≈ 34 for m = 10 MeV, ⟨σv⟩ = 10^-22 cm^3/s (using Eq. (23) and the standard radiation-dominated H). The linearized integration over ln(Tdec/TCMB) ≈ 12 therefore corresponds to multiple annihilations per initial DM particle, violating number conservation. A simple energy-conservation bound gives the maximum N_nth from converting the entire DM rest energy at T_dec as (8/7)(11/4)^{4/3} ρDM(T_dec)/ργ(T_dec) ≈ 7×10^-4, whereas Eq. (16) gives 0.024 at m = 1 MeV, ⟨σv⟩ = 10^-24 and 0.2-0.4 in the plotted region of Fig. 2. Late-time release has more leverage, but the annihilation rate per Hubble time Γ/H ∝ T is largest at T_dec, so a self-consistent solution cannot approach the quoted values. The correct treatment must solve the coupled equations for nDM(t) and ρnth(t) including the −⟨σv⟩n^2 depletion term; this will suppress the log-enhanced growth of Eq. (16) and likely make the relic-annihilation constraints subdominant to the neutrino-detector bounds, undermining the central claim of competitive constraints.
  2. [Section II, Eqs. (11)-(13)] There is an independent normalization error in the source term. As defined in Eq. (11), Cν = ⟨σv⟩m n^2 is already the total energy release rate for a self-conjugate DM particle: for a real scalar, the annihilation rate per volume is (1/2)⟨σv⟩n^2 and each annihilation releases energy 2m, giving ⟨σv⟩m n^2. The additional factor of 2 in Eq. (13), said to account for neutrinos and antineutrinos, therefore double-counts the energy release. For Dirac fermion DM with nDM as the total particle-plus-antiparticle density (the normalization implied by Eq. (23) and by nDM = ρDM/m), the annihilation rate is ⟨σv⟩n^2/4 and the energy release rate is ⟨σv⟩m n^2/2, so the product 2Cν in Eq. (13) overestimates the source by a factor of 4. This shifts the N_nth bounds in Fig. 1 to larger cross sections by at least a factor of 2, further weakening the claimed limits. This issue is distinct from the depletion problem and affects the Dirac-panel results specifically.
minor comments (4)
  1. [Section II, text near Eqs. (13) and (16)] The numerical value Tdec = 10 keV is described as the moment of completion of non-instantaneous neutrino decoupling, but neutrino decoupling is typically completed around T ≈ 1–2 MeV; 10 keV is closer to the end of e+e− annihilation when the Tν/Tγ ratio freezes. Clarify the distinction, and if 10 keV is intended as the start of the integration for N_nth, state so explicitly.
  2. [Eq. (12) vs. Eq. (23)] Eq. (12) expresses Cν in terms of (T/0.1 MeV)^6 while Eq. (23) uses (T/0.01 MeV)^3 for nDM; the coefficient c presumably absorbs this mismatch, but the inconsistency makes it difficult for the reader to reproduce Eq. (16) from the preceding equations. Please align the temperature scalings and state the units of c explicitly.
  3. [Fig. 1 and Fig. 2 captions] The captions do not explicitly distinguish the curves representing N_nth bounds from the vertical lines representing N_th mass bounds; the text explains this, but the figures would be much clearer with labels such as 'N_nth bound' and 'N_th mass bound' directly in the panels.
  4. [Section II, paragraph after Eq. (16)] The statement that varying Tdec and TCMB by an order of magnitude changes N_nth at the O(0.1)% level is not obviously consistent with the logarithmic dependence in Eq. (16), where a factor-of-10 change in either limit changes ln(Tdec/TCMB) by about 2.3 for one of the limits. Please specify which ratio is being varied and what is held fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's Neff predictions are externally benchmarked and no fitted parameter is renamed as a prediction.

full rationale

The paper's central derivation is self-contained against external data. The thermal contribution N_th^eff is computed from the coupled Boltzmann equations for T_nu and T_gamma following Ref. [29], with inputs only the DM mass, spin, and standard thermodynamics; the measured Neff values from Planck, DESI, SPT-3G, and ACT are taken from outside the paper and are not used to tune any parameter. The nonthermal contribution N_nth^eff is computed from Eq. (13), integrating the collision rate C_nu = <sigma v> m_DM n_DM^2 with n_DM fixed by Eq. (22)-(23) to the observed relic density; no parameter is fitted to the Neff data, and the resulting exclusion curves in Fig. 1 are genuine predictions for given (m_DM, <sigma v>). The paper does not invoke any uniqueness theorem, and its self-citations (e.g., Ref. [36] for CMB spectral distortions, Ref. [21] for neutrino-portal DM production) are illustrative or background, not load-bearing. The strongest possible concern, that Eq. (13) neglects DM depletion from the annihilation that generates the nonthermal energy, is a physical correctness or self-consistency issue about the assumed production mechanism, not a case where a 'prediction' reduces by construction to its own input; hence it does not constitute circularity under the stated criteria. Overall, the derivation chain is externally benchmarked and the score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper's constraints rest on the standard cosmological expansion, the free-streaming of neutrinos after decoupling, the non-relativistic dark matter assumption, and the non-standard late-time production premise that permits cross sections above the thermal value. The thermal contribution is inherited from Ref. [29]. No new particles or forces are introduced.

free parameters (3)
  • Tdec = 10 keV
    Lower integration bound for the nonthermal energy release (Eq. 13); chosen as the end of non-instantaneous neutrino decoupling. The result is logarithmically insensitive to this choice, so it is not a fitted parameter but a chosen boundary.
  • TCMB = 0.1 eV
    Upper integration bound for the nonthermal energy release; chosen at recombination. The result is logarithmically insensitive to this choice.
  • g_rho, g_s = 3.34
    Effective relativistic degrees of freedom used after neutrino decoupling (Eqs. 14-15). Approximation justified by the QCD phase transition; affects the normalization of the nonthermal contribution by a constant factor.
assumptions (5)
  • standard math Radiation-dominated Friedmann expansion with H ≈ 1.66 sqrt(g_rho) T^2 / M_Pl after QCD transition
    Used in Eq. (14) for the Hubble rate in the Boltzmann equation for the nonthermal energy release.
  • domain assumption After neutrino decoupling, neutrinos free-stream and injected energy accumulates as nonthermal energy density without thermalizing
    Basis for Eq. (10) and the entire nonthermal treatment; if neutrinos were still coupled, the energy injection would be described by the thermal equations (5)-(6).
  • domain assumption DM is non-relativistic during the epoch of interest, so p_DM ≈ 0 and the annihilation cross section is velocity-independent
    Used in Eq. (7) and around Eq. (11) to express the energy density as mDM nDM and to treat the cross section as a constant.
  • ad hoc to paper The DM relic density today is produced by a late-time mechanism so that the annihilation cross section can exceed the standard freeze-out value while matching ΩDM h^2 = 0.12
    Discussed in Sec. III; the entire bounds apply only in such non-standard production scenarios, and the paper does not quantify how generic this assumption is.
  • domain assumption For ⟨σv⟩ > ⟨σv⟩th, DM stays in thermal equilibrium with neutrinos throughout the decoupling epoch, so the thermal contribution N_th_eff from Ref. [29] applies
    Invoked in Sec. II before Eq. (5); the freeze-out temperature depends only logarithmically on the cross section, which is the stated justification.

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Cite this review

Pith. "Pith review of Bounds and detection of MeV-scale dark matter annihilation to neutrinos." pith.science (2026). https://pith.science/paper/M625V3EF

@misc{pith2026250604568,
  author       = {Pith},
  title        = {Pith review of: Bounds and detection of MeV-scale dark matter annihilation to neutrinos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M625V3EF}},
  note         = {Machine review of arXiv:2506.04568}
}
read the original abstract

Current and most upcoming neutrino detectors can only reach a dark matter annihilation cross section to neutrinos larger than the standard freeze-out value, but they open intriguing detection avenues for non-standard dark matter paradigms. An important corollary of these non-standard scenarios is relic dark matter annihilation after neutrino decoupling, which was previously overlooked in constraining MeV-scale dark matter. However, by combining the contributions from entropy injection during neutrino decoupling and from nonthermal neutrino energy release after decoupling, we derive significant constraints on the annihilation cross section to neutrinos, which in some mass regimes become stronger than the current bounds. Furthermore, we find that the lower bounds on dark matter masses become inconclusive under the recent data releases from the DESI, SPT-3G, and ACT collaborations. These bounds determine the extent to which upcoming neutrino detectors will probe dark matter annihilation into neutrinos.

Figures

Figures reproduced from arXiv: 2506.04568 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Limits on thermal real scalar DM annihilation to neutrinos [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.