Neutron Decay Anomaly Model

• The paper identifies a 1% discrepancy between bottle and beam neutron lifetimes, suggesting exotic decay channels or oscillation effects as possible explanations.
• It systematically evaluates dark-decay, mirror-oscillation, and beam-systematic models using detailed experimental constraints from proton counting, neutron stars, and relic abundance.
• The analysis bridges precision measurement challenges with theoretical modeling, guiding future experiments to resolve the neutron lifetime anomaly.

Searching arXiv for the cited neutron anomaly papers to ground the article in current and primary-source literature. arXiv_search({"query":"id:(Klopf et al., 2019) OR id:(Tan, 2023) OR id:(Broussard et al., 2021) OR id:(Fornal et al., 2018) OR id:(Bastero-Gil et al., 2024) OR id:(Das et al., 14 May 2025)", "max_results": 10, "sort_by": "submittedDate", "sort_order": "descending"}) Searching more broadly for recent arXiv work on neutron lifetime anomaly interpretations and constraints. arXiv_search({"query":"neutron lifetime anomaly dark decay mirror neutron charge exchange beam bottle", "max_results": 10, "sort_by": "submittedDate", "sort_order": "descending"}) In the literature summarized here, the neutron decay anomaly model denotes a family of hypotheses developed to explain the persistent mismatch between free-neutron lifetimes extracted from bottle and beam experiments. Reported averages typically place bottle measurements near $878$–$880$ s and beam measurements near $888$ s, so the discrepancy is described as an $\sim 1\%$ effect at $3.6\sigma$ to $4\sigma$, depending on the compilation (Klopf et al., 2019, Serebrov et al., 2020, Tan, 2023). The main explanatory strategies are: an additional neutron decay branch into dark-sector final states, oscillations into mirror-sector states, and beam-specific proton-loss systematics.

1. Empirical structure of the anomaly

Bottle experiments measure the inclusive disappearance time of trapped ultracold neutrons, whereas beam experiments infer a lifetime from a counted decay channel, usually via protons or electrons produced in a defined neutron flux. This immediately creates a phenomenological distinction: a genuinely new non-$\beta$ neutron loss channel shortens bottle lifetimes, while a beam-specific proton-counting inefficiency lengthens beam lifetimes. The dark-decay interpretation expresses the needed extra branching fraction as

$$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$

which is quoted as approximately $0.95\%$, $0.9\%$, or $880$0 in different analyses because the adopted lifetime averages differ slightly (Fornal et al., 2018, Grinstein et al., 2018, Darini, 2022).

A complementary formulation appears in beam-systematic analyses. If a fraction $880$1 of decay protons is not registered, then

$880$2

so a percent-level proton loss directly mimics the observed anomaly (Serebrov et al., 2020).

Model class	Core mechanism	Representative status
Dark-decay models	$880$3 at $880$4	Visible channels strongly constrained
Mirror-oscillation models	$880$5 conversion	Some variants excluded; high-field variants still proposed
Beam-systematic models	Proton loss in beam traps	Remain experimentally testable

This classification suggests that the anomaly is not a single model but a constrained problem in inverse phenomenology: one must explain a percent-level shift while remaining compatible with nuclear stability, neutron-star structure, direct decay searches, and beamline systematics.

2. Dark-decay constructions

The original dark-decay program, developed by Fornal and Grinstein, proposed that the neutron could decay into one or more dark-sector particles without a proton in the final state. Representative channels are $880$6, $880$7, and $880$8, with kinematics tightly restricted by proton stability and by the requirement that bound neutrons in stable nuclei, especially $880$9Be, not undergo analogous decays (Fornal et al., 2018). For the visible $888$0 mode, the allowed mass interval quoted in the PERKEO II analysis is

$888$1

so scanning $888$2 is equivalent to scanning for a monoenergetic line in the summed $888$3 kinetic energy between $888$4 and $888$5 keV (Klopf et al., 2019).

Two-body invisible decays introduce a dark fermion $888$6 and a dark boson $888$7, typically with

$888$8

In one scalar-mediated realization, the combined constraints from neutron lifetime, relic abundance, neutron stars, Higgs physics, and Big Bang Nucleosynthesis restrict the scalar mass to

$888$9

with $\sim 1\%$0 GeV and a thermal freeze-out coupling $\sim 1\%$1 (Bastero-Gil et al., 2024). That construction uses Higgs-portal mixing to generate a repulsive neutron–dark-matter Yukawa interaction, precisely because unprotected neutron conversion inside neutron stars otherwise softens the equation of state too strongly.

A distinct line of work replaces $\sim 1\%$2 by a minimal assignment $\sim 1\%$3, allowing

$\sim 1\%$4

At nucleon level the interaction is modeled by

$\sim 1\%$5

and the central kinematic parameter is $\sim 1\%$6 (Strumia, 2021, Darini, 2022). A key model-building point is that with more than one $\sim 1\%$7 generation the decay width can scale as $\sim 1\%$8 rather than $\sim 1\%$9, which permits fitting the anomaly while suppressing crossed-process constraints such as $3.6\sigma$0 (Darini, 2022).

A further variant uses scalar leptoquarks as a portal to a dark scalar $3.6\sigma$1, producing the channel $3.6\sigma$2. In that model $3.6\sigma$3 and $3.6\sigma$4 are scalar leptoquarks in the $3.6\sigma$5 representation, $3.6\sigma$6 is a complex scalar with $3.6\sigma$7 and $3.6\sigma$8, and the effective hadronic coupling takes the form

$3.6\sigma$9

with a benchmark $4\sigma$0 MeV and leptoquark masses near $4\sigma$1 TeV (Khatibi, 2023). That construction is unusual in simultaneously targeting the neutron anomaly, freeze-in dark matter, muon $4\sigma$2, and $4\sigma$3.

3. Oscillation-based models

Oscillation explanations replace an actual decay branch by coherent conversion into a sterile or mirror-sector state. In the ordinary–mirror neutron framework, the mirror basis $4\sigma$4 is related to the mass basis $4\sigma$5 through

$4\sigma$6

and the vacuum oscillation probability is

$4\sigma$7

(Tan, 2023). In traps, incoherent wall reflections reset the phase, so the oscillation channel becomes an effective disappearance rate,

$4\sigma$8

where $4\sigma$9 is the mean free-flight time. The same review argues that beam experiments are almost insensitive because

$\beta$0

well below current beam precision (Tan, 2023).

The favored parameter region in that mirror-matter phenomenology is

$\beta$1

which implies an intrinsic oscillation timescale of order ns and resonant magnetic fields

$\beta$2

(Tan, 2023). The same framework uses geometry-dependent collision frequencies to explain why small or narrow magnetic traps can yield much shorter apparent storage lifetimes than large traps.

This proposal must be distinguished from an earlier non-degenerate mirror-neutron model that attributed a $\beta$3 beam bias to resonant conversion inside the $\beta$4 T NIST beam-lifetime solenoid. A dedicated SNS disappearance/regeneration search in a $\beta$5 T peak field found no signal, obtained $\beta$6 at $\beta$7 CL, and excluded the full parameter band that would produce the required $\beta$8 lifetime increase for $\beta$9 neV (Broussard et al., 2021). The current mirror-neutron literature therefore contains both excluded and still-proposed regimes, separated mainly by the required resonance scale.

4. Experimental constraints and exclusions

Direct searches have sharply reduced the viable space for visible dark decays. For $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$0, a Los Alamos search for monoenergetic $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$1 rays ruled out this channel as the sole explanation of the anomaly with $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$2 CL (Klopf et al., 2019). For $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$3, UCNA obtained

$$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$4

for $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$5, thereby excluding the channel as the sole explanation at the $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$6 level, while PERKEO II extended sensitivity to lower energies (Klopf et al., 2019).

The PERKEO II reanalysis searched for a narrow line in the summed coincidence spectrum between $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$7 and $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$8 keV. At $$B_{\rm dark}=1-\frac{\tau_{\rm bottle}}{\tau_{\rm beam}},$$9 CL it excluded a $0.95\%$0 branching fraction from $0.95\%$1 keV to the kinematic endpoint, covering $0.95\%$2 of the allowed $0.95\%$3-mass range; at better than $0.95\%$4 local significance it excluded the $0.95\%$5 hypothesis from $0.95\%$6 keV to the endpoint, covering $0.95\%$7 of the allowed mass window (Klopf et al., 2019). The remaining low-energy corner survives mainly because the analysis required both detectors to trigger, which reduces acceptance for very low-$0.95\%$8 events.

Other dark-decay realizations encounter orthogonal constraints. If the dark fermion is Majorana, two $0.95\%$9 insertions induce $0.9\%$0-$0.9\%$1 oscillations; in the explicit analysis of that scenario, the coupling needed for a $0.9\%$2 dark branching implies $0.9\%$3 s, in violent conflict with the experimental lower limit $0.9\%$4 s (Leontaris et al., 2018). By contrast, invisible $0.9\%$5 models with $0.9\%$6 dark generations were constructed precisely so that matching $0.9\%$7 need not violate Kamiokande, SNO, and KamLAND neutron-disappearance bounds (Darini, 2022).

A broader phenomenological conclusion also emerges from global analyses based on the storage-method lifetime and precision $0.9\%$8: exotic neutron decays are bounded at

$0.9\%$9

which strongly disfavors any explanation that requires a full percent-level exotic branch unless the input value of $880$00 moves away from the most accurate measurements (Klopf et al., 2019).

5. Neutron stars, relic abundance, and dark-sector consistency

Neutron-star structure is the most severe consistency test for dark-decay explanations. If free neutrons can convert into a dark fermion $880$01 in dense matter, the equation of state typically softens and the maximum mass falls below the observed $880$02 scale. One route around this is repulsive dark matter–baryon cross-interactions. In a mean-field treatment with

$880$03

the threshold for keeping stars nearly pure neutron matter is $880$04 MeV for SLy-4 and $880$05 MeV (Grinstein et al., 2018). A benchmark with $880$06 eV, $880$07, $880$08, and $880$09 MeV preserves $880$10 (Grinstein et al., 2018).

A separate analysis of the Fornal–Grinstein channel $880$11, using $880$12 MeV and $880$13 MeV, treats $880$14 as a self-interacting fermion gas and $880$15 as a trapped Bose-condensed boson. In that framework the neutron-star constraints require a repulsive $880$16-$880$17 vector interaction of approximately

$880$18

to keep $880$19, and the trapped boson must satisfy

$880$20

to avoid overheating old stars (Husain et al., 2023). The same paper notes that extragalactic background light and X-ray bounds can be even stronger for photon-coupled dark bosons.

The scalar-mediated thermal dark-matter realization sharpens the combined parameter space further. There, $880$21 GeV, $880$22, and the full set of neutron-lifetime, relic-density, neutron-star, Higgs, and BBN constraints compresses the light scalar into the narrow interval

$880$23

(Bastero-Gil et al., 2024). This is a particularly restrictive result because it simultaneously encodes direct-decay search limits and dense-matter stability.

Recent relativistic mean-field work revisits the same issue with $880$24 MeV and no explicit $880$25-baryon portal, writing

$880$26

for the dark fermion chemical potential (Das et al., 14 May 2025). In that analysis $880$27 softens the equation of state catastrophically and gives $880$28, whereas stiff and intermediate hadronic equations of state become viable for $880$29 of order $880$30–$880$31. Soft hadronic equations of state are effectively excluded once neutron-star and cluster self-scattering bounds are imposed (Das et al., 14 May 2025).

The $880$32 scenario changes this logic because chemical equilibrium becomes $880$33 rather than $880$34. Both the effective-theory treatment and the explicit BSk24 analysis find that $880$35 softens the neutron-star equation of state only mildly, so stars near $880$36 remain allowed (Strumia, 2021, Darini, 2022). This difference is structural: the dense-matter cost of populating three light baryon-number-$880$37 fermions is much smaller than that of populating one nearly degenerate baryon-number-1 fermion.

6. Beam-systematic interpretations and current outlook

An entirely different explanation attributes the anomaly to proton losses in beam experiments. The central process is charge exchange on residual gas,

$880$38

which neutralizes the trapped proton; the resulting fast neutral hydrogen escapes the electrostatic and magnetic trap, while the molecular ion may fail to register because of detector dead layers or timing cuts (Serebrov et al., 2020, Serebrov et al., 2020). In the detailed trap model,

$880$39

so the inferred beam lifetime shifts as

$880$40

for $880$41 (Serebrov et al., 2020).

Using $880$42 mbar, $880$43 K, $880$44 K, and a $880$45C bakeout composition, one analysis finds

$880$46

with unbaked and $880$47C-baked cases giving $880$48 and $880$49, respectively (Serebrov et al., 2020). A later reanalysis argues that an $880$50-only residual gas, once the finite timing window is included, can still generate a $880$51 s downward correction; if the actual in-trap pressure were only $880$52 times the nominal warm reading, the correction would reach $880$53 s, i.e. essentially the full anomaly (Serebrov et al., 2020). These papers also emphasize that elastic scattering at $880$54 mbar is negligible and that dead-layer corrections alone would move the beam result upward, not downward (Serebrov et al., 2020, Serebrov et al., 2020).

Taken together, the literature indicates a sharply stratified status. Percent-level visible dark-decay explanations are now largely excluded; Majorana dark-fermion realizations are excluded by $880$55-$880$56 oscillation bounds; neutron-star structure severely restricts baryon-number-1 dark sectors unless additional repulsion is built in; one class of mirror-neutron beam explanations has been experimentally excluded, while another class explicitly moves the resonance scale to $880$57–$880$58 T; and residual-gas charge exchange remains a quantitatively testable beam-systematic alternative (Klopf et al., 2019, Broussard et al., 2021, Tan, 2023, Serebrov et al., 2020). The anomaly therefore persists less as a single viable model than as a constrained intersection of neutron decay phenomenology, dense-matter astrophysics, and precision beam instrumentation.