Neutron Dark Decay Models

• Neutron dark decay is the hypothesis that neutrons decay into dark-sector states via nonstandard channels, potentially explaining the lifetime anomaly.
• The decay processes operate within a narrow kinematic window near the neutron mass, leading to channel-specific experimental searches across radiative and fully dark modes.
• Baryonic portal models link dark matter candidates with nuclear and neutron-star phenomena, demanding novel interactions to reconcile laboratory and astrophysical constraints.

Searching arXiv for relevant papers on neutron dark decay, constraints, and reviews. Neutron dark decay is the hypothesis that the neutron possesses one or more beyond-Standard-Model decay channels into dark-sector states, in addition to ordinary beta decay. It was formulated as a possible resolution of the long-standing beam–bottle neutron lifetime discrepancy by allowing a branching fraction of order $1\%$ into final states with no proton, while simultaneously opening a portal between baryons and dark matter candidates. In the literature, the subject has evolved from a narrow explanation of the lifetime anomaly into a broader framework linking nuclear stability, halo-nucleus decays, baryonic portal model building, self-interacting dark matter, neutron-star structure, and, more recently, gravitational-wave and compact-object phenomenology (Fornal et al., 2018, Fornal et al., 2020, Fornal, 2023).

1. Origin in the neutron lifetime anomaly

The immediate motivation is the mismatch between two classes of free-neutron lifetime measurements. Bottle experiments count surviving ultracold neutrons and therefore measure the total decay width, whereas beam experiments count decay protons and therefore measure only the partial width into proton-producing channels. The discrepancy is about $8$–$9$ s, corresponding to roughly a $1\%$ effect and a significance at the level of about $4\sigma$. In this interpretation, bottle experiments measure $\Gamma_n$, beam experiments measure $\Gamma_\beta$, and the relation

$\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$

implies ${\rm Br}(n\to p+\text{anything})\approx 0.99$ and ${\rm Br}(n\to \text{dark})\approx 0.01$ if the anomaly is due to a dark channel (Fornal et al., 2020, Fornal, 2023).

In its modern usage, neutron dark decay denotes processes such as

$8$0

or more generally $8$1 dark-sector states with at least one new invisible degree of freedom. A historical precursor predating the lifetime-anomaly proposal studied sub-GeV dark fermions $8$2 coupled through baryon-number-violating neutron-portal operators and showed that decays such as $8$3 and $8$4 can mimic standard nucleon-decay signatures while having different kinematics (Davoudiasl, 2014). The 2018 anomaly-driven literature, however, shifted the emphasis to percent-level branching ratios, tightly constrained masses, and explicit consistency with nuclear and astrophysical data (Fornal et al., 2018).

A recurring theme is that neutron dark decay need not be synonymous with proton instability or unrestricted baryon-number violation. Several explicit constructions assign baryon number $8$5 to the dark fermion so that $8$6 conserves baryon number, while other constructions realize effectively baryon-number-violating operators at low energy. The distinction is model dependent and materially affects both neutron-star phenomenology and laboratory bounds (Motta et al., 2018, Fornal et al., 2018).

2. Kinematics, mass windows, and channel taxonomy

Any viable dark final state must fit into a very narrow kinematic window below the neutron mass. A standard summary is

$8$7

where $8$8 is the total invariant mass of the dark final state and the upper limit is $8$9. This lower bound comes from forbidding dark decays of neutrons bound in stable nuclei, especially $9$0, and also protects proton stability because $9$1 (Fornal et al., 2020). Earlier versions of the bound, such as $9$2 MeV, arose from a slightly different treatment of the $9$3 threshold; a refinement using the prompt decay of $9$4 into two $9$5 particles raises the lower limit by $9$6 keV to $9$7 MeV (Pfützner et al., 2018).

For the two-body radiative mode $9$8, the allowed dark-fermion mass window is

$9$9

and if $1\%$0 is itself stable dark matter one further requires

$1\%$1

which implies a monochromatic photon with

$1\%$2

For the fully dark mode $1\%$3, the condition becomes

$1\%$4

If both $1\%$5 and $1\%$6 are stable dark-sector states, one also needs

$1\%$7

to prevent decays of one dark particle into the other plus Standard-Model states (Fornal et al., 2020, Fornal et al., 2018).

This narrow kinematic band has two consequences. First, the decay products are necessarily almost degenerate with the neutron, so in dense matter the conversion $1\%$8 is controlled primarily by chemical potentials rather than large vacuum mass splittings. Second, laboratory searches are highly channel specific: a photon mode, an $1\%$9 mode, and a fully dark mode populate different corners of the same narrow mass strip and are not interchangeable experimentally (Fornal, 2023).

3. Baryonic portals and model-building realizations

The simplest anomaly-driven realizations use a baryonic portal between quarks and a dark fermion. In the original Fornal–Grinstein constructions, a colored scalar $4\sigma$0 generates, after being integrated out, a small neutron–dark-fermion mixing term $4\sigma$1. One model yields $4\sigma$2 through the neutron magnetic dipole coupling, while a second introduces an additional dark fermion $4\sigma$3 and scalar $4\sigma$4, leading to $4\sigma$5. The low-energy widths scale with $4\sigma$6 and with the near-threshold phase space, and matching the anomaly requires $4\sigma$7 (Fornal et al., 2018). These constructions also formalized the now-standard baryon-number assignments $4\sigma$8, $4\sigma$9, $\Gamma_n$0, $\Gamma_n$1, which forbid proton decay while allowing neutron dark decay (Fornal et al., 2020).

A more elaborate realization embeds the decay into a hidden $\Gamma_n$2 sector with a heavy baryon $\Gamma_n$3, a Dirac dark fermion $\Gamma_n$4, a scalar baryon $\Gamma_n$5, and a light vector mediator $\Gamma_n$6. The neutron portal

$\Gamma_n$7

maps below $\Gamma_n$8 onto $\Gamma_n$9, and after integrating out $\Gamma_\beta$0 one obtains an effective coupling

$\Gamma_\beta$1

The same dark fermion $\Gamma_\beta$2 can be a thermal relic, the same light vector $\Gamma_\beta$3 can mediate repulsive self-interactions, and the benchmark

$\Gamma_\beta$4

yields transfer cross sections resembling ETHOS-4 and a damping scale $\Gamma_\beta$5 (Karananas et al., 2018).

Other portals exist. A scalar-leptoquark construction generates

$\Gamma_\beta$6

with a complex scalar dark matter candidate $\Gamma_\beta$7 carrying $\Gamma_\beta$8 and $\Gamma_\beta$9. After integrating out two scalar leptoquarks, the effective operator is

$\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$0

and the invisible branching fraction can again be of order $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$1, while the relic abundance is produced by freeze-in rather than freeze-out (Khatibi, 2023). The broader lesson is that neutron dark decay is not a single model but a family of baryonic portals whose UV completions differ in whether they emphasize radiative decay, purely dark decay, dark matter freeze-out, freeze-in, or correlated flavor anomalies.

4. Nuclear probes and direct laboratory searches

Laboratory searches have progressively carved away the simplest visible channels. A dedicated Los Alamos ultracold-neutron search for the monochromatic photon in $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$2 covered

$\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$3

and excluded a $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$4 branching ratio over that range at about $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$5. Later reinterpretations including Borexino constraints from hydrogen stability further restricted the parameter space, leaving branching fractions $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$6 unconstrained and photon energies below $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$7 MeV experimentally unexplored (Fornal et al., 2020). Searches for $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$8 similarly excluded a $\Gamma_n=\Gamma_\beta+\Gamma_{\rm dark}$9 branching ratio for total pair energies above ${\rm Br}(n\to p+\text{anything})\approx 0.99$0 keV, and PERKEO improved that threshold to ${\rm Br}(n\to p+\text{anything})\approx 0.99$1 keV (Fornal, 2023).

Bound neutrons in weakly bound nuclei provide a complementary probe because the same neutron–dark mixing can induce nuclear decays with strikingly clean signatures. The basic nuclear condition is

${\rm Br}(n\to p+\text{anything})\approx 0.99$2

so only nuclei with very small neutron separation energy ${\rm Br}(n\to p+\text{anything})\approx 0.99$3 are relevant. Halo nuclei such as ${\rm Br}(n\to p+\text{anything})\approx 0.99$4, ${\rm Br}(n\to p+\text{anything})\approx 0.99$5, ${\rm Br}(n\to p+\text{anything})\approx 0.99$6, and ${\rm Br}(n\to p+\text{anything})\approx 0.99$7 were identified as candidate systems, with ${\rm Br}(n\to p+\text{anything})\approx 0.99$8 singled out as especially promising because ${\rm Br}(n\to p+\text{anything})\approx 0.99$9 can be studied by accelerator mass spectrometry through the long-lived daughter ${\rm Br}(n\to \text{dark})\approx 0.01$0 (Pfützner et al., 2018).

The most stringent dedicated nuclear bound currently summarized here comes from the search

${\rm Br}(n\to \text{dark})\approx 0.01$1

performed at GANIL with a ${\rm Br}(n\to \text{dark})\approx 0.01$2 beam and the TETRA neutron detector. No time-correlated neutron excess was found, leading to

${\rm Br}(n\to \text{dark})\approx 0.01$3

and, within the original Fornal–Grinstein framework, to an upper bound on the free-neutron dark branching ratio of order

${\rm Br}(n\to \text{dark})\approx 0.01$4

over favorable ranges of ${\rm Br}(n\to \text{dark})\approx 0.01$5 (Joubioux et al., 2023). This is substantially below the ${\rm Br}(n\to \text{dark})\approx 0.01$6 level required by the lifetime anomaly, and it illustrates why halo nuclei are regarded as unusually sensitive probes.

Dark-decay models also imply nonstandard annihilation channels if the halo contains ${\rm Br}(n\to \text{dark})\approx 0.01$7. In two benchmark anomaly-motivated models, ${\rm Br}(n\to \text{dark})\approx 0.01$8 annihilation can yield

${\rm Br}(n\to \text{dark})\approx 0.01$9

or multi-$8$00 final states. These signatures can be reinterpreted within neutron–antineutron oscillation and proton-decay searches at Super-Kamiokande, Hyper-Kamiokande, and DUNE, because the visible hadronic final states resemble standard rare-event topologies even though their origin is different (Keung et al., 2019).

5. Neutron stars, dark matter, and dense-matter constraints

The strongest theoretical pressure on neutron dark decay has come from neutron-star structure. In the minimal picture, once the dark fermion is nearly degenerate with the neutron, neutron-star matter reaches chemical equilibrium

$8$01

and the dark component fills a Fermi sea at the expense of neutron matter. Because weakly interacting $8$02 particles provide much less pressure than strongly interacting neutrons at the same energy density, the equation of state softens sharply. Using APR and QHC18 equations of state, Baym et al. showed that a stable, feebly interacting dark fermion in equilibrium with baryons drives the maximum neutron-star mass down to

$8$03

well below observed neutron-star masses (Baym et al., 2018). A QMC-based calculation of the specific $8$04 scenario found an analogous result: direct TOV integration gives $8$05, while enforcing conservation of total baryon number in the conversion from an ordinary star to a dark-enriched one lowers the realistic maximum to

$8$06

In that same analysis, restoring $8$07 required

$8$08

which was argued to be incompatible with dark matter self-interaction bounds if $8$09 is the dominant cosmological dark matter component (Motta et al., 2018).

These exclusions apply most directly to minimal models with a single, stable, feebly interacting dark fermion. Non-minimal dark sectors can evade them by adding repulsion. One explicit realization uses a light vector mediator in the hidden sector, giving self-interacting dark matter with

$8$10

which satisfies a lower bound from neutron-star stability,

$8$11

while simultaneously reproducing the relic abundance and small-scale-structure phenomenology (Karananas et al., 2018). Another construction employs a light scalar mediator $8$12 and a Higgs portal, so that the combined effect of dark-matter self-interactions and an effective repulsive neutron–dark interaction can support heavy neutron stars; the combined neutron-lifetime, relic-density, neutron-star, Higgs, and BBN constraints then restrict the mediator to

$8$13

in the most constrained version of the model (Bastero-Gil et al., 2024).

More recent work has broadened the neutron-star analysis in two directions. First, the role of the nuclear symmetry energy has been emphasized: in $8$14-stable matter with neutrons, protons, electrons, and dark fermions, the symmetry-energy slope and the dark-sector couplings jointly determine radii and tidal deformabilities, and suitable combinations can remain compatible with current $8$15, NICER, and GW170817 constraints (Divaris et al., 29 Aug 2025). Second, dark-decay phenomenology has been connected to oscillation modes and exotic compact objects. In a QMC analysis of $8$16, repulsive self-interaction parameterized by

$8$17

was found to be required to recover $8$18 stars, and the resulting $8$19-mode frequencies followed universal relations similar to nucleon-only stars (Husain, 23 May 2025). A subsequent compact-object study proposed that if neutron dark decay is suppressed above densities of a few times saturation density, one can simultaneously accommodate heavy neutron stars and subsolar-mass compact objects such as HESS J1731-347 while keeping the decay active at lower densities (Vikiaris et al., 4 Feb 2026).

6. Present status, misconceptions, and open problems

The present status is structurally asymmetric across model space. The simplest percent-level visible channels are heavily constrained: $8$20 has been excluded at the $8$21 level over the conventional photon window, $8$22 is excluded at the $8$23 level over most accessible pair energies, and halo-nucleus searches now probe well below the anomaly scale in the original Fornal–Grinstein radiative framework (Joubioux et al., 2023, Fornal et al., 2020). Minimal neutron-star implementations with a single stable, feebly interacting dark fermion are likewise excluded by the existence of heavy neutron stars (Baym et al., 2018, Motta et al., 2018).

That does not imply that every neutron dark decay model is ruled out. A common misconception is to identify the entire subject with the already constrained $8$24 channel. The literature instead distinguishes between radiative modes, $8$25 modes, fully dark two-body decays, dark sectors with conserved baryon number, models in which the dark state is only a subcomponent of cosmological dark matter, and models in which repulsive self-interactions or neutron–dark interactions suppress the softening of neutron-star matter (Fornal, 2023). A second misconception is that neutron dark decay necessarily violates baryon number; several of the explicit models conserve baryon number by assigning $8$26 to the dark fermion (Motta et al., 2018, Khatibi, 2023).

Open problems remain on both the laboratory and astrophysical sides. Precision beam and bottle measurements, including the Los Alamos UCNProBe concept of measuring the proton branching ratio directly in a trapped-neutron setup, remain decisive for the lifetime anomaly itself (Fornal et al., 2020). Nuclear searches with halo nuclei beyond $8$27 can test complementary mass windows (Joubioux et al., 2023). In dense matter, the extent to which the putative vacuum decay channel survives, is blocked, or is modified by in-medium effects remains unsettled; recent work explicitly characterizes this as an open problem entangled with uncertainties in the high-density symmetry energy and with possible additional phases such as hyperons or quark matter (Divaris et al., 29 Aug 2025). Gravitational-wave asteroseismology and improved compact-object mass–radius measurements add a new observational axis for testing the repulsive-interaction mechanisms invoked to rescue non-minimal models (Husain, 23 May 2025, Vikiaris et al., 4 Feb 2026).

Neutron dark decay therefore persists as a tightly constrained research program rather than a single surviving model. Its central idea—a percent-level baryonic portal to a nearly degenerate dark state—remains technically sharp because the allowed masses, visible energies, and dense-matter effects all occupy narrow windows. That sharpness is precisely what has made the subject both vulnerable to exclusion and unusually fertile as a probe of dark sectors, baryon portals, and strongly gravitating matter (Fornal et al., 2018, Fornal, 2023).