Constraining invisible neutrino decays with the cosmic microwave background

Georg Raffelt (Max Planck Inst.; Munich); Steen Hannestad (University of Aarhus)

REVIEW

Constraining invisible neutrino decays with the cosmic microwave background

Steen Hannestad (University of Aarhus), Georg Raffelt (Max Planck Inst., Munich)

High Energy Physics - Phenomenology · Submitted 26 Sep 2005 · 28 references

Pith's verdict: A clean, honest constraint paper: the off-diagonal Majoron bound in Eq. (7) is real, and its four-orders-of-magnitude margin survives the schematic treatment.

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arXiv IDhep-ph/0509278 (version 1)

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CitationGeorg Raffelt (Max Planck Inst., Munich), Steen Hannestad (University of Aarhus). "Constraining invisible neutrino decays with the cosmic microwave background." arXiv:hep-ph/0509278 (2005). https://pith.science/paper/72PTYHVZ

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Short version: this is a clean constraint paper, and the number that matters — g < 0.6e-11 (50 meV/m)^2 for off-diagonal couplings — is real. The chain is transparent: take the known free-streaming requirement at decoupling, write down the decay/coalescence transport rate, require it below H_dec. Nothing is fitted to the quantity being bounded, so there is no circularity to worry about. The reader's ACCEPT is right, and the stress-test note's direction is right too — see below on why the bound is conservative rather than aggressive. What is actually new is the translation into Yukawa bounds, especially Eq. (7), and the corollary in Eq. (9): Majoron decays cannot be responsible for non-standard flavor ratios in cosmic-ray neutrinos, because the required coupling sits four orders of magnitude above the bound. The diagonal bound (Eq. 4) is not much of an advance; the authors themselves say it is comparable to SN 1987A. The value is concentrated in the off-diagonal result. Credit where due: the transport argument — one Lorentz factor for time dilation, two for angular randomization — is correct and is properly credited to Chacko et al. [12]. The authors also explicitly decline to claim the diffuse supernova neutrino background is unaffected, which is the right call given how crude the bound is. Soft spots, in proportion. The whole analysis is dimensional: no Boltzmann equation, no CMB likelihood. The authors call the criterion 'somewhat schematic' and the limit 'crude,' so this is acknowledged, not hidden — the classifier's 'limitations: none found' is simply wrong on that point. The coefficient in Eq. (7) inherits order-one uncertainty from E = 3T and the angular average, and the authors do not quantify it for the off-diagonal case. That is a minor complaint, not a load-bearing one: the four-orders-of-magnitude margin in Eq. (9) survives any plausible factor. If anything the bound is conservative — the true free-streaming criterion for acoustic-peak modes is Gamma < k c_s, and k c_s sits well below H_dec at decoupling, so using H_dec gives a weaker limit than a mode-by-mode treatment would. One small thing I would have liked: the claim that the pseudoscalar coupling is conservative for binary processes is asserted rather than shown. Minor. Who should read it: anyone working on secret neutrino interactions, Majoron models, or high-energy neutrino flavor. It is a four-page paper that does one thing well. Recommendation: send it out. It is the kind of short, careful constraint paper that earns its citations, and referees should focus on the order-one factors in Eq. (7) rather than on the structure.

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Major objections (2)

[Sec. II, Eqs. (2)–(4)] The binary rate g⁴T is quoted without specifying which channel dominates and whether φ is assumed to be thermalized. The νν → νν channel via φ exchange requires no φ in the bath, but νφ → νφ and νν̄ → φφ do. For g ~ 10⁻⁷ the φ decoupling temperature is of order eV, i.e. near T_ν,dec = 0.18 eV, so the assumption matters at the factor-of-few level for the diagonal bound and for the comparison with SN 1987A. The paper should state the assumption explicitly. If φ is in equilibrium, the independent N_eff constraint from one massless bosonic degree of freedom (ΔN_eff ≈ 0.57) is comparable to current sensitivities and is not discussed; it should at least be noted as a separate constraint on the same coupling.
[Sec. III, Eqs. (6)–(7)] The (m/E)³ transport factor is the load-bearing step for the headline coefficient, and the paper does not state whether the approximations (E = 3T_ν,dec, angular average ⟨1−cosθ⟩ ≈ (m/E)²/2, neglect of Pauli blocking and of the thermal distribution) make the bound conservative or aggressive. The authors acknowledge that the criterion is 'somewhat schematic' (Sec. II) and that the limit is 'crude' (Sec. IV), but for the off-diagonal number no direction is given. A sentence stating the sign of the expected correction, or a factor-of-few uncertainty band on 0.61×10⁻¹¹, would make the headline number usable. This does not threaten the four-orders-of-magnitude conclusion of Eq. (9), which is the paper's main qualitative claim.

Minor objections (6)

[Sec. II, paragraph after Eq. (4)] The statement 'E ≈ 3T_ν,rec ≈ 1 eV' is inconsistent with T_ν,dec = 0.18 eV quoted two paragraphs earlier, for which 3T = 0.54 eV; the subscript 'rec' should presumably be 'dec'. Fix the number and the subscript.
[Eq. (1)] State that g_jk is Hermitian and whether the coupling is to Dirac or Majorana neutrinos, since the ν → ν̄' + φ channel summed in Eq. (5) depends on this choice.
[Sec. II] State explicitly that φ is assumed massless or with m_φ ≪ eV, and how the bounds scale if m_φ ≳ T_ν,dec, where the decay channel is kinematically suppressed.
[Sec. III, Eq. (8)] The (δm²)³/m⁶ suppression for quasi-degenerate pairs is mentioned but not propagated into a numerical statement. Since the cosmic-ray application in Sec. IV relies on it, give the relaxed bound explicitly for the light pair.
[Sec. IV] The inference that Majorons 'interact too weakly to be trapped in a SN core' is stated more strongly than the schematic bound supports; consider softening it to match the stated uncertainty of the limit.
[References] Ref. [4] contains the typo 'microwave nackground'; Ref. [2] is missing its opening quotation mark; the accent rendering in 'Tom` as' and the spacing in 'acknowled ged' and 'diﬀus e' should be fixed in the final version.

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The paper

The paper claims

The cosmic microwave background requires neutrinos to free-stream at decoupling, which caps secret neutrino couplings at about $10^{-11}$.

The reading

The paper asks whether the cosmic microwave background can reveal how strongly ordinary neutrinos interact with hypothetical very light pseudoscalars such as Majorons. If neutrinos stayed coupled to such particles at photon decoupling, they would not free-stream, and the acoustic peaks would carry a different imprint; the authors turn that requirement into upper bounds on the neutrino-pseudoscalar Yukawa couplings. For diagonal couplings they find $g < 1.1 times 10^{-7}$, comparable to the supernova 1987A limit. For off-diagonal couplings with hierarchical masses they find $g < 0.61 times 10^{-11}(50,mathrm{meV}/m)^2$, strong enough to exclude $nu to nu' + phi$ decays as a way to change the flavor mix of high-energy cosmic-ray neutrinos on their way to Earth.

What carries the argument

The load-bearing mechanism is a comparison between the cosmic expansion rate at decoupling, $H_{rm dec}=2.81 times 10^{-29},mathrm{eV}$, and a transport rate for $nu leftrightarrow nu' + phi$: $Gamma_T simeq frac{g^2}{16pi} m (m/E)^3$ with $E=3T_{nu,rm dec}$. The $(m/E)^3$ factor is what makes the bound so strong: one power is Lorentz time dilation of the decay, and two powers account for the small-angle random walk needed to change the neutrino's direction because the decay products are nearly collinear. Requiring $Gamma_T < H_{rm dec}$ yields the off-diagonal limit; for diagonal couplings the authors instead use the binary scattering estimate $Gamma_{1+2leftrightarrow3+4} sim g^4 T$ and compare it with the same expansion rate.

Extended reading notes

Core claim

The central claim is that the measured acoustic peaks require neutrinos to be free-streaming at photon decoupling, when the photon temperature is about $0.256,mathrm{eV}$, and that this requirement places bounds on secret neutrino interactions at eV energies far below direct laboratory reach. For a pseudoscalar coupling $-i phi sum_{jk} g_{jk} bar{nu}_j gamma_5 nu_k$, the diagonal couplings are bounded at $g < 1.1 times 10^{-7}$ from binary scattering, while the off-diagonal couplings are bounded much more tightly because single decay and coalescence processes scale as $g^2$ rather than $g^4$. Using hierarchical neutrino masses with the heavier mass $m simeq 50,mathrm{meV}$, the authors obtain $g < 0.61 times 10^{-11}(50,mathrm{meV}/m)^2$. This is about four orders of magnitude below the coupling that would be needed for $nu to nu' + phi$ to modify the expected $1:1:1$ flavor ratio of high-energy cosmic-ray neutrinos at Earth.

Load-bearing premise

The load-bearing premise is that the CMB free-streaming requirement can be represented by the single schematic inequality $Gamma_T < H_{rm dec}$, using the collinear-suppressed transport rate and ignoring order-one numerical factors.

Original abstract

Precision measurements of the acoustic peaks of the cosmic microwave background indicate that neutrinos must be freely streaming at the photon decoupling epoch when T ~ 0.3 eV. This requirement implies restrictive limits on ``secret neutrino interactions,'' notably on neutrino Yukawa couplings with hypothetical low-mass (pseudo)scalars \phi. For diagonal couplings in the neutrino mass basis we find g < 1 x 10^-7, comparable to limits from supernova 1987A. For the off-diagonal couplings and assuming hierarchical neutrino masses we find g < 1 x 10^-11 (0.05 eV/m)^2 where m is the heavier mass of a given neutrino pair connected by g. This stringent limit excludes that the flavor content of high-energy neutrinos from cosmic-ray sources is modified by \nu -> \nu' + \phi decays on their way to Earth.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,413 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Precision measurements of the acoustic peaks of the cosmic microwave background indicate that neutrinos must be freely streaming at the photon decoupling epoch when T ~ 0.3 eV. This requirement implies restrictive limits on ``secret neutrino interactions,'' notably on neutrino Yukawa couplings with hypothetical low-mass (pseudo)scalars \phi. For diagonal couplings in the neutrino mass basis we find g < 1 x 10^-7, comparable to limits from supernova 1987A. For the off-diagonal couplings and assuming hierarchical neutrino masses we find g < 1 x 10^-11 (0.05 eV/m)^2 where m is the heavier mass of a given neutrino pair connected by g. This stringent limit excludes that the flavor content of high-energy neutrinos from cosmic-ray sources is modified by \nu -> \nu' + \phi decays on their way to Earth.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Precision measurements of the acoustic peaks of the cosmic microwave background indicate that neutrinos must be freely streaming at the photon decoupling epoch when T ~ 0.3 eV.	background 0.75	0.10	0.13	hedged possibility 0.68
s1	This requirement implies restrictive limits on ``secret neutrino interactions,'' notably on neutrino Yukawa couplings with hypothetical low-mass (pseudo)scalars \phi.	interpretation 0.95	0.34	0.23	asserted 0.98
s2	For diagonal couplings in the neutrino mass basis we find g < 1 x 10^-7, comparable to limits from supernova 1987A.	result 1.00	0.93	0.20	asserted 1.00
s3	For the off-diagonal couplings and assuming hierarchical neutrino masses we find g < 1 x 10^-11 (0.05 eV/m)^2 where m is the heavier mass of a given neutrino pair connected by g.	result 1.00	0.93	0.20	asserted 1.00
s4	This stringent limit excludes that the flavor content of high-energy neutrinos from cosmic-ray sources is modified by \nu -> \nu' + \phi decays on their way to Earth.	interpretation 0.94	0.71	0.49	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from analysis of existing data 0.80.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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Invisible neutrino decays are bounded to lifetimes above about 10^9 seconds (scaled by neutrino mass cubed) by Planck 2018 data, and above 10^-3 seconds by Big Bang nucleosynthesis.
Neutrinophilic Axion-Like Dark Matter
hep-ph 2018-09 conditional novelty 4.0 of 10

A derivative axion-neutrino coupling would shift oscillation probabilities by an amount DUNE can probe down to roughly 10^-11 per GeV, with tighter bounds from cosmology.
Updated constraints on non-standard neutrino interactions from Planck
astro-ph.CO 2013-11 conditional novelty 4.0 of 10

Planck data bound neutrino self-interactions to GX below (0.06 GeV)^-2 and pseudoscalar couplings to about 1e-7 (diagonal) and 2e-11 (off-diagonal decay), while ruling out permanently strongly interacting neutrinos at...
Constraints on neutrino -- dark matter interactions from cosmic microwave background and large scale structure data
astro-ph.CO 2009-11 conditional novelty 4.0 of 10

Combining WMAP five-year and SDSS data, the authors bound the neutrino-dark matter scattering opacity to roughly 10^-42 to 10^-40 cm^2 MeV^-1, with the limit tightening as the interacting dark matter fraction grows.
Are cosmological neutrinos free-streaming?
astro-ph 2008-06 conditional novelty 4.0 of 10

Cosmological data require neutrinos to stream freely by redshift about 1500, bounding their coupling to a majoron-like scalar to g below about 1e-7 and the decay lifetime above about 1e10 s.
Status of Oscillation plus Decay of Atmospheric and Long-Baseline Neutrinos
hep-ph 2008-02 conditional novelty 4.0 of 10

Combining atmospheric and long-baseline neutrino data, the authors find no significant evidence for invisible neutrino decay and set a 99% CL lower bound on the lifetime of the heaviest neutrino of 9.3e-11 s/eV.
Feebly Interacting Particles: FIPs 2022 workshop report
hep-ph 2023-05 accept novelty 3.0 of 10

The FIPs 2022 workshop report surveys the theory, astrophysical bounds, and planned experiments for feebly interacting particles below the GeV scale, and argues for a diversified multi-laboratory program over the next decade.
Tau Neutrinos in the Next Decade: from GeV to EeV
hep-ph 2022-03 accept novelty 3.0 of 10

A community whitepaper maps the current and planned tau neutrino program across accelerator, collider, atmospheric, and astrophysical experiments, and identifies the cross-section, propagation, and reconstruction tool...
High-Energy and Ultra-High-Energy Neutrinos
hep-ph 2022-03 accept novelty 2.0 of 10

High-energy and ultra-high-energy astrophysical neutrinos offer a unique window on beyond-Standard-Model physics and on the sources of ultra-high-energy cosmic rays, and the paper lays out the detector program needed ...
Neutrino masses and mixings and...
hep-ph 2006-06 accept novelty 2.0 of 10

The review consolidates the evidence that solar and atmospheric neutrino deficits are explained by three-neutrino oscillations with large mixing angles, and surveys remaining anomalies and theoretical models.
Non Thermal Features in the Cosmic Neutrino Background
astro-ph 2006-03 unverdicted novelty 1.0 of 10

A review of current cosmological bounds on distortions of the cosmic neutrino background, concluding that present data only weakly constrain non-thermal features and future experiments will tighten some, but not all, ...
Massive neutrinos and cosmology
astro-ph 2006-03 accept novelty 1.0 of 10

A detailed review of how cosmological observations bound the sum of neutrino masses through the free-streaming suppression of small-scale structure, and of future sensitivity forecasts.

How later papers used it

69 later papers cite it

Evidence: substantial. 66 of the citing papers share no author with it, and 12 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 130 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper

Followed this paper in order to calculate the effective neutrino decay rate that erases the neutrino anisotropic stress.

Cosmological Constraints on Invisible Neutrino Decays Revisited (2019) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

65 arXiv papers cite this in 122 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 72 sentences without a confident label

Contests it 3 papers

In fact, it has never been demonstrated rigorously that the exponential damping of anisotropic stress assumed in the analyses of [ref] is even a phenomenology of relativistic neutrino decay or its most constraining observable in the cosmological context.

Invisible neutrino decay in precision cosmology · Introduction · contest 0.75
This result is in contrast to the rate $Γ_T ∼(m_ν/E_ν)^3 (1/τ_0)$ employed in previous analyses [ref] , which is based upon a heuristic but (as we shall show) incorrect random walk argument.

Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime · Introduction · contest 0.80
This supersedes previous analyses using heuristic arguments to model the rate at which neutrino freestreaming is suppressed [ref] .

Global view of neutrino interactions in cosmology: The freestreaming window as seen by Planck · Neutrino Interaction Models and comparison with the literature · contest 0.77

Builds on it 1 paper

This leads to the bound [ref] [equation] In the event of the decay taking place in a thermal distribution of light neutrinos and pseudoscalars we need to take the second term in Eq. [ref] into account.

Decaying neutrinos: The long way to isotropy · A more general case · 0.89

Uses its method or tool 1 paper

Ref. [ref] argues that $< Γ> ≃Γ (m_ν/E_ν)^3$, which by thermally averaging $< m/E>$ and $< m^2/E^2>$ separately yields: [equation] Written as a function of the scale factor $a$, the neutrino lifetime and the neutrino mass, reads: [equation] where $a_0 = 1$.

Cosmological Constraints on Invisible Neutrino Decays Revisited · Modeling neutrino decays · 0.91

Uses its data or values 8 papers

This leads to the bound [ref] : |Z^ν_ii|<1.2×10^-7 .

Testing Moduli and Flavon Dynamics with Neutrino Oscillations · Limits on neutrino coupling · 0.93
This requirement translates into [ref] |g_ii| ≲ 10^-7 , |g_ij| ≲ 0.61 ×10^-11 (0.05 eV/m_ν_j)^2 ,for $i ≠j$ and $m_ν_j>m_ν_i$.

Soft supersymmetry breaking as the sole origin of neutrino masses and lepton number violation · Majoron-neutrino couplings · 0.80
Here we adopt the bound [ref] (see also [ref] )[This is the case with a generic flavor violation for the $ϕ$ coupling.

Cosmic Stability of Dark Matter from Pauli Blocking · C$ν$B free-streaming and DM stabilized by neutrino sea · 0.87

Cites it as support 1 paper

In fact, for $g ≲10^-7$, the massless pesudo-scalar $ϕ$ will never be in thermal equilibrium via the two-body scattering before the CMB formation, as demonstrated in Refs. [ref] .

Helicity-changing Decays of Cosmological Relic Neutrinos · Observational Constraints · 0.98

Cites it as background 26 papers

The first CMB constraint on neutrino decay [ref] had been derived by simply demanding that neutrinos must remain free-streaming up to the time of recombination at $z = z^*$.

Invisible neutrino decay in precision cosmology · Transport rate · 0.89
The impact of exotic neutrino interactions in cosmology, and in particular in the CMB, have been studied in various contexts, including scenarios in which: neutrinos have self-interactions that arise from heavy mediators [ref] , neutrinos annihilate into massless scalars [ref] , neutrinos decay into light particles [ref] , and neutrinos temporarily thermalize with $eV-$scale neutrino-philic scalars [ref] .

Precision CMB constraints on eV-scale bosons coupled to neutrinos · Introduction · 0.98
The cosmological impact of putative neutrino self interactions has been widely studied [ref] , and lately there has been a renewed interest due to their possible relationship to the Hubble tension [ref] or the short baseline neutrino anomalies [ref] .

Long Range Interactions in Cosmology: Implications for Neutrinos · Introduction · 0.95

Discussion

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