A gap is a place to look
Where the Missing Neutrons Could Go
Read as a missing decay, the gap between the original beam and bottle averages needs a 0.946% branch. Rebuild the proposal, set two pair-decay scenarios against UCNA's published bound, and test whether any final state has room for it.
We propose to explain this anomaly by a dark decay channel for the neutron, involving one or more dark sector particles in the final state.
Bartosz Fornal and Benjamín Grinstein, 2018. A proposed explanation, not a dark-particle detection. Read the proposal ↓
The claim at full strength
Two clocks. A possible missing branch.
Suppose bottle disappearance measures all neutron decays, while the beam method counts the proton-producing branch. Then a decay without a proton makes the beam lifetime look longer. This is the proposal’s hypothesis, not something the subtraction proves.
Printed: a gap of approximately 8.4 s, 4.0 σ, a proton-producing branch of approximately 99% and so a dark branch of approximately 1%. Recomputed: 8.4 s, 4.02 σ, 99.054% and 0.946%. The dark branch is 0.0541 percentage points below the approximate claim.
Published inputs and approximate headline. The quoted averages are the historical inputs throughout this page. The later erratum leaves the lifetime relation unchanged ↓
Put the control in your hands
What comes out matters.
Switch the proposed pair channel. The same published bound meets a very different prediction.
Set the share in the gap budget ↓
Kinetic energy excludes the electron and positron rest masses. 322 keV is one of the two signal energies UCNA simulated in its Figure 4. The other, 644 keV, is the kinematic endpoint and lies on the summary’s open boundary, so this engine would refuse it.
At the historical central lifetimes
Loading the frozen record
Overall dark-decay explanation: OPEN, as of 2026-09-22. This comparison addresses one final state under the stated model.
UCNA reports a branch limit below 0.0001 of all neutron decays (0.01%), at greater than 90% confidence, for 100 keV < K_pair < 644 keV.
UCNA abstract and published analysis ↓
Every numerical bound comparison assumes UCNA’s uniform three-body phase-space acceptance model and a single nearly monoenergetic summed pair kinetic energy. A different interaction, angular distribution or broad spectrum needs a validated response of its own.
The actual upper limit is below the published ceiling. A fixed prediction reaching the ceiling is therefore constrained. A prediction below the ceiling could still exceed the actual limit: this summary alone cannot say. INCONCLUSIVE here means not decided by this summary, never allowed.
The original paper gives the photon scenario an accompanying pair branch of at most 1.1e-6 of all decays (0.00011%). It separately proposes a dominant pair channel at approximately 1%. The companion value is a maximum, not a fixed prediction at each mass.
Both scenarios in the original proposal ↓The control on the control
How much of the check can we check?
Grade B: this comparison trusts UCNA's published sensitivity analysis. We could not rerun the experimental control or test an injected signal.
B_required / U = 0.009459459459 / 0.0001 = 94.5946. This is a ratio to a ceiling on a published upper limit, not a significance or a discovery probability.
UCNA also reports ≫5σ exclusion for its 1% dominant-pair hypothesis. That is the experiment's result. This page neither recomputes it nor rescales it to 0.946%.
No observations were planted and no signal was recovered. The frozen control record contains a published limit summary, without foreground counts, background counts, a response or a reusable likelihood. Independent confirmation by injection and recomputation of the experimental control are both unavailable.
The published analysis supplies the confidence and acceptance, including resolution and the energy search. A ratio to its ceiling supplies no measured discovery probability.
OPEN · as of 2026-09-22
Read as a missing decay, the historical lifetime gap needs a 0.946% dark branch: UCNA constrains the searched pair channel, the beta-decay relation leaves room for the whole branch with only one of four axial-coupling values compared here (aSPECT’s), and the general explanation remains open.
The 2026 PDG neutron listing still distinguishes the beam and ultracold-neutron results. Its ultracold-neutron average is 878.3 ± 0.4 s, as printed. It marks Gonzalez 2021 superseded by Musedinovic 2025. This is current context, not an input to the historical calculation.
The proposal’s own Note added acknowledges both the photon challenge and the dominant-pair exclusion, and notes that photon energies below 0.782 MeV remained unexplored. The proposal led with the photon channel, which its conclusions call “the most striking signature”, and it also allowed wholly invisible final states. The authors’ 2020 review adds that photon branches up to about 0.1% are not constrained by the Los Alamos photon data at any dark-matter mass. Their response is part of the record; it is not independent evidence of a dark decay.
Original Note added · The authors’ review · Later review · Independent pair search
A test that sees no final state
A second test sees no final state at all. Through the Standard Model link between the neutron’s lifetime and its axial coupling, Czarnecki, Marciano and Sirlin, using their favoured axial coupling, bounded all exotic decays together below 0.27% at one-sided 95% confidence, and Dubbers et al. wrote that the dark-decay explanation “can be excluded with a high level of confidence”. The claimants reply that aSPECT’s lower axial coupling puts the Standard Model lifetime at the beam value. Run live below, the relation leaves room for the whole 0.946% branch with only one of four axial-coupling values compared here (aSPECT’s).
Neutron stars constrain the proposal’s models separately. Fornal’s 2023 review reports that in the two minimal models neutron stars could not exceed 0.8 solar masses, well below the 2 solar masses of some observed neutron stars, so the models gained repulsive dark-sector interactions; the original Note added already pointed to that route. The 2026 dense-matter paper in the sources continues this model building.
Run the beta-decay test ↓ · Czarnecki, Marciano and Sirlin · Dubbers et al. · Claimant reply · Dense-matter model building
Is the gap itself real?
The claimants’ reviews called the proton-counting beam experiment at NIST and the electron-counting beam experiment at J-PARC complementary, and in 2023 judged the early J-PARC data not yet precise enough to favour either side. In December 2024 the J-PARC group reported 877.2 ± 1.7 (stat.) +4.0/−3.6 (sys.) s from counting decay electrons, which they describe as consistent with the bottle method and in 2.3σ tension with the proton-counting beam average. Its arXiv record carries no journal reference, and the frozen 2026 PDG listing does not include it. This page combines it with nothing.
A 2026 paper by Desai argues that pressure-dependent detector effects plausibly explain the large χ² values and the dependence on gas pressure in the J-PARC data; its abstract gives no corrected lifetime. The measurement and the critique both concern the lifetime itself; neither searches for a dark final state.
On the proton-counting side, the NIST group tested one proposed way to lose protons, charge exchange with molecular hydrogen in the proton trap, and found the NIST beam result “unlikely to have been significantly affected” by it (Caylor et al., 2025). NIST’s summary of that work, dated 28 January 2026, says: “We still don’t know the reason why the discrepancy exists.” Whether the gap is real is the other half of this question, and it is still argued.
Electron-counting beam result · Pressure-dependence critique · Molecular-hydrogen check · NIST summary · Claimant review on complementary beam methods
What would change this
An independently replicated non-proton decay, at a rate that accounts for the lifetime discrepancy, would support this explanation. A resolved measurement bias that removes the discrepancy would remove this motivation. A settled axial coupling would decide the beta-decay test: near aSPECT’s value the relation leaves room for the branch, and near PERKEO III’s it does not. Additional channel searches narrow particular models; agreement of lifetimes would not rule out every arbitrarily small exotic decay.
Go deeper / a conditional gap budget
How little of the gap can pairs carry?
At the historical central lifetimes, for a single narrow pair signal inside UCNA’s 100 to 644 keV window and under its published signal model and confidence, the searched pair channel can supply less than 0.0888 s of the 8.4 s gap. More than 8.3112 s requires another explanation.
The corresponding pair share is less than 1.05714% of the proposed dark branch. This is this page’s conditional algebraic translation, not a new experimental limit.
Historical central values
The same calculation at every sensitivity corner
The smaller-gap corner raises the bottle lifetime by its quoted error and lowers the beam lifetime by its quoted error. The larger-gap corner does the reverse. These are deterministic sensitivity cases, not a joint confidence region. Their uncertainties are not multiplied by UCNA’s confidence.
| Case | Bottle (s) | Beam (s) | Required branch | Pair share ceiling | Pair gap ceiling | Remaining gap floor |
|---|
A small maximum contribution does not establish invisible decays. The remainder could reflect other channels, a measurement bias or another explanation. The bound cannot be applied separately to many parts of a broad spectrum and summed into a new total limit. The next section asks whether any final state at all has room for the branch.
The receipt includes your choices, full precision results, strict inequalities, source versions, acceptance assumptions and the Grade B limitation. It is created locally.
Go deeper / a test that sees no final state
Can any final state carry the branch?
A dark decay of any kind, whatever it produced, would leave the lifetime for ordinary beta decay longer than the bottle’s total lifetime. The Standard Model ties that beta-decay lifetime to the axial coupling λ, which experiments measure from the angles and energies of decay products rather than from any lifetime: τ_β(1 + 3λ²) = 5172.0 ± 1.1 s, with the constant set by V_ud from superallowed nuclear decays and the radiative corrections. If the proposal is right, this third clock reads the beam value, 888.0 s. If there is no dark branch, it reads the bottle value, 879.6 s.
Czarnecki, Marciano and Sirlin’s own inputs go through the same functions first. A trap lifetime of 879.4 ± 0.6 s and g_A = 1.2755 ± 0.0011 give an ordinary branch of 0.99990 ± 0.00071 before the g_A term (printed 0.9999(7)), a slope of 1.301 per unit of g_A (printed 1.30), and a one-sided 95% bound on all exotic decays together of 0.273% (printed < 0.27%), which is 2.41 s of their 8.6 s puzzle (printed 2.4 s). Truncating the distribution at a zero branch, as Dubbers et al. do, gives 0.320% (printed 0.32%).
Calculating
Axial coupling used
Implied exotic branch, all final states together
One-sided upper points, two published conventions
| Source | |λ| | Beta-decay clock (s) | Implied exotic branch | Upper point, Gaussian | Upper point, truncated | Decision |
|---|
The claimants answer this test directly. Fornal’s 2023 review sets PERKEO III’s |λ| = 1.27641 against aSPECT’s 1.2677 ± 0.0028 and concludes: “The PERKEO III result agrees with the bottle average, but the aSPECT experiment is consistent with the beam average, favoring the neutron dark decay proposal as a solution to the neutron lifetime puzzle.” The two values differ by 3.1 combined standard errors, so which one is right decides this test. Dubbers et al., writing before aSPECT’s final result and noting that its preliminary value would not significantly change their conclusion, found that the dark-decay explanation “can be excluded with a high level of confidence” and gave a bound of 0.28%.
Conditions: ordinary decay follows the Standard Model; V_ud from superallowed decays and CKM unitarity are negligibly affected by the new physics, as Czarnecki et al. assume; the errors are independent and Gaussian. The constant is theirs, from 2018; Dubbers et al. reach 5172.3 ± 1.1 s by a route that avoids the universal radiative correction. This page remeasures nothing. It applies the published relation to published values of λ with this page’s historical bottle lifetime, and it calls a result decided only when both published bound conventions agree.
Czarnecki, Marciano and Sirlin ↓ · Dubbers et al. ↓ · PERKEO III ↓ · aSPECT ↓ · PDG axial coupling ↓ · Claimant reply ↓
Visible apparatus
The check
Waiting for the local engine.
The 4.02 σ calculation divides the 8.4 s difference by the quadrature error 2.088061 s, treating the two published errors as independent. This checks the historical summary arithmetic, not the underlying lifetime analyses or a current combined fit.
Anchor tolerances: 0.05 s for the gap and 0.05 for significance, from rounding to one decimal. The approximate branch tolerance is 0.1 percentage points, a declared page convention rather than an experimental error. That convention alone cannot separate Equation (1) from treating the beam value as the total lifetime, which would give 0.955%, so the verifier also pins the branch to the exact fraction 7/740 within 1e-12.
A fault in the input must change the answer
Choices, uncertainties and refusals
Your choices are the pair hypothesis, the kinetic-energy case, a custom pair share (a logarithmic control from 0.01% to 100%, with presets), a lifetime sensitivity corner, and the value of λ in the beta-decay relation. The historical anchor always stays fixed. The companion maximum stays fixed too. Display rounding and the logarithmic scales do not change decisions. No efficiency or confidence knob is supported.
Outside the open kinetic-energy interval, or for photons, invisible modes, total pair energy, a different acceptance model, unsupported units or a broad spectrum, the engine refuses this bound comparison and clears its numeric answer. Invalid fractions and nonpositive lifetimes are refused. A nonpositive missing branch cannot be divided into an allocation budget. The beta-decay relation accepts only its frozen sources of λ and positive, finite values, and withholds its comparisons if it cannot reproduce the published bound.
Not applicable: this proposal interprets two published lifetime averages. It is not a selected peak whose search procedure can be run on comparable null records here. Equal lifetimes give a zero branch as an algebra check only; no false-positive rate is claimed.
The experimental work this page cannot repeat
Recomputed here: the historical anchor, both outcomes of the ceiling rule, the conditional gap budgets and the beta-decay relation’s published bound. Not recomputed: UCNA’s confidence limit or any measurement of λ. Not run: a signal injection and recovery. The machine-readable ledger retains both limitations.
Read the claim ledger · Read the live engine · Source terms
Open the frozen input records
- Historical lifetime and model statements
- UCNA bound, units and acceptance scope
- Other searches and claimant responses
- PDG edition and licence
- PDG mean-life summary
- PDG listing and supersession notes
- Beta-decay relation, bound conventions and claimant reply
- PDG axial-coupling average
- PDG axial-coupling listing
Lifetime inputs: proposal, physical PDF page 1 and Equation (1). Both pair cases: physical page 3. Claimant response: Note added and conclusions, physical page 5. UCNA: abstract, phase-space model on physical page 4, bound on physical page 5. Beta-decay relation: Czarnecki et al., Equations (3) and (12) to (14); Dubbers et al., physical pages 8 and 9; claimant reply, Fornal 2023, printed pages 15 and 16. λ values: the frozen PDG 2026 listing and summary. No plotted points were digitised.
Published numbers are attributed factual transcriptions. PDG responses are frozen under CC BY 4.0. The proposal’s published article is CC BY 4.0; its arXiv version has separate terms. Czarnecki et al. and Dubbers et al. are CC BY 4.0 according to their publisher records. UCNA’s article and figures are not redistributed. Every diagram here is generated from the stated arithmetic.
The record behind the instrument
Bartosz Fornal and Benjamín Grinstein (2018), Dark Matter Interpretation of the Neutron Decay Anomaly, Physical Review Letters 120, 191801. DOI: 10.1103/PhysRevLett.120.191801. Numerical version: arXiv:1801.01124v3.
Versioned proposal PDF · Published article and termsX. Sun et al. (UCNA Collaboration, 2018), Search for dark matter decay of the free neutron from the UCNA experiment: n → χ + e+e−, Physical Review C 97, 052501(R). DOI: 10.1103/PhysRevC.97.052501. Numerical version: arXiv:1803.10890v1.
Versioned experimental paperF. Takahashi et al. (Particle Data Group, 2026), Review of Particle Physics, International Journal of Modern Physics A 41, 2630011. Neutron mean-life listing S017T.
PDG listing · Edition metadataBartosz Fornal and Benjamín Grinstein (2020), Neutron's Dark Secret, Modern Physics Letters A 35, 2030019. DOI: 10.1142/S0217732320300190. arXiv:2007.13931v1.
Claimant reviewBartosz Fornal (2023), Neutron Dark Decay, Universe 9, 449. DOI: 10.3390/universe9100449. arXiv:2306.11349v1.
Later claimant reviewZ. Tang et al. (2018), Search for the Neutron Decay n→X+γ, Where X is a Dark Matter Particle, Physical Review Letters 121, 022505. DOI: 10.1103/PhysRevLett.121.022505.
Accepted manuscript for the final resultM. Klopf, E. Jericha, B. Märkisch, H. Saul, T. Soldner and H. Abele (2019), Constraints on the Dark Matter Interpretation n → χ + e+e− of the Neutron Decay Anomaly with the PERKEO II experiment, Physical Review Letters 122, 222503. DOI: 10.1103/PhysRevLett.122.222503. arXiv:1905.01912v2.
PERKEO II paperBartosz Fornal and Benjamín Grinstein (2020), Erratum: Dark Matter Interpretation of the Neutron Decay Anomaly, Physical Review Letters 124, 219901(E). DOI: 10.1103/PhysRevLett.124.219901.
The magnetic-moment correction in the later erratum changes model coefficients, not the lifetime relation used here. The historical search boundaries on this page are not a present-day allowed-mass map.
ErratumY. Fuwa, T. Hasegawa, K. Hirota et al. (31 authors, 2024), Improved measurements of neutron lifetime with cold neutron beam at J-PARC. arXiv:2412.19519v1, submitted 27 December 2024.
Versioned preprintAshish M. Desai (2026), Pressure-dependent detector effects in beam-based neutron lifetime measurements, The European Physical Journal A 62, 154. DOI: 10.1140/epja/s10050-026-01929-x.
Published articleM. Vikiaris, V. Petousis, M. Veselsky and Ch. C. Moustakidis (2026), Neutron dark decay and exotic compact objects, Physical Review D 114, 043032. DOI: 10.1103/21p6-sqfh.
Recent theoretical work continues to study conditional dark-decay models in dense matter. That is neither a laboratory detection nor evidence that every dark-decay model survives all other constraints.
Publisher abstract, the extent checked hereAndrzej Czarnecki, William J. Marciano and Alberto Sirlin (2018), Neutron Lifetime and Axial Coupling Connection, Physical Review Letters 120, 202002. DOI: 10.1103/PhysRevLett.120.202002. Numerical version: arXiv:1802.01804v3.
Versioned paper · Published articleD. Dubbers, H. Saul, B. Märkisch, T. Soldner and H. Abele (2019), Exotic decay channels are not the cause of the neutron lifetime anomaly, Physics Letters B 791, 6-10. DOI: 10.1016/j.physletb.2019.02.013. arXiv:1812.00626v3.
Versioned paper · Published articleB. Märkisch, H. Mest, H. Saul, X. Wang, H. Abele, D. Dubbers, M. Klopf, A. Petoukhov, C. Roick, T. Soldner and D. Werder (2019), Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam, Physical Review Letters 122, 242501. DOI: 10.1103/PhysRevLett.122.242501. arXiv:1812.04666v1.
Versioned paperM. Beck et al. (aSPECT, 18 authors, 2020), Improved determination of the beta-antineutrino angular correlation coefficient a in free neutron decay with the aSPECT spectrometer, Physical Review C 101, 055506. DOI: 10.1103/PhysRevC.101.055506. arXiv:1908.04785v2.
Versioned paperF. Takahashi et al. (Particle Data Group, 2026), Review of Particle Physics, International Journal of Modern Physics A 41, 2630011. Neutron listing S017AV, λ ≡ g_A / g_V, as printed -1.2753 ± 0.0013.
PDG summary · PDG listingJ. Caylor, R. Biswas, B. Crawford, M. S. Dewey, N. Fomin, G. L. Greene, S. F. Hoogerheide, J. Hungria-Negron, H. P. Mumm, J. S. Nico, F. E. Wietfeldt, D. O. Valete and J. Zuchegno (2025), Detection of molecular hydrogen in a neutron beam lifetime experiment, Physical Review C 112, 065501. DOI: 10.1103/nr3b-3dtl. arXiv:2506.01682v2.
Versioned preprint · Published articleNational Institute of Standards and Technology (2026), Spotlight: Electromagnetic Proton Trap at the NIST Center for Neutron Research (NCNR), news item dated 28 January 2026.
NIST news item
What is new here, and what is not
The lifetime relation and experimental limits belong to the cited literature. The further result here is the reader-operated allocation budget, conditional on those records.
we searched the Wasteland index, web results, arXiv-linked papers, GitHub search results and the Liu Lab lifetime-puzzle page on 2026-09-22 and did not find a public interactive page combining the original lifetime-branch calculation with UCNA's conservative pair-channel allocation ceiling and an explicit distinction between constrained and not decided by the published summary.