---
title: Neutron Decay Anomaly Model
url: https://www.emergentmind.com/topics/neutron-decay-anomaly-model
type: topic
---

# Neutron Decay Anomaly Model

Searching arXiv for the cited neutron anomaly papers to ground the article in current and primary-source literature.
arXiv_search({"query":"id:1905.01912 OR id:2302.07805 OR id:2111.05543 OR id:1801.01124 OR id:2403.08666 OR id:2505.09190", "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 [1905.01912][2003.02092][2302.07805]. 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 \(1.1\%\) in different analyses because the adopted lifetime averages differ slightly [1801.01124][1811.06546][2212.04998].

A complementary formulation appears in beam-systematic analyses. If a fraction \(f_{\rm loss}\) of decay protons is not registered, then
\[
\lambda_{\rm meas}=(1-f_{\rm loss})\,\lambda_{\rm true}, \qquad
\tau_{\rm meas}\approx \frac{\tau_{\rm true}}{1-f_{\rm loss}}\approx \tau_{\rm true}(1+f_{\rm loss}),
\]
so a percent-level proton loss directly mimics the observed anomaly [2011.13272].

| Model class | Core mechanism | Representative status |
|---|---|---|
| Dark-decay models | \(n\to \chi+X\) at \(\sim 1\%\) | Visible channels strongly constrained |
| Mirror-oscillation models | \(n\leftrightarrow n'\) 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 \(n\to \chi+\gamma\), \(n\to \chi+\phi\), and \(n\to \chi+e^+e^-\), with kinematics tightly restricted by proton stability and by the requirement that bound neutrons in stable nuclei, especially \({}^{9}\)Be, not undergo analogous decays [1801.01124]. For the visible \(e^+e^-\) mode, the allowed mass interval quoted in the PERKEO II analysis is
\[
937.900~{\rm MeV}\le m_\chi \le 938.543~{\rm MeV},
\]
so scanning \(m_\chi\) is equivalent to scanning for a monoenergetic line in the summed \(e^+e^-\) kinetic energy between \(0\) and \(644\) keV [1905.01912].

Two-body invisible decays introduce a dark fermion \(\chi\) and a dark boson \(\phi\), typically with
\[
937.900~{\rm MeV}<m_\chi+m_\phi<939.565~{\rm MeV}.
\]
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
\[
2m_e < m_\phi < 2m_e+0.0375~{\rm MeV},
\]
with \(m_\chi\approx 1\) GeV and a thermal freeze-out coupling \(g_\chi\simeq 0.053\) [2403.08666]. 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 \(B_\chi=1\) by a minimal assignment \(B_\chi=1/3\), allowing
\[
n\to \chi\chi\chi.
\]
At nucleon level the interaction is modeled by
\[
\mathcal{L}_{\rm eff}= \mathcal{L}_{\rm SM}+\bar\Psi(i\slashed{\partial}-M)\Psi
+\frac{(\bar\Psi^c\Gamma\Psi)(\bar n\Gamma\Psi)+{\rm h.c.}}{3!\,\Lambda_{\chi n}^2},
\]
and the central kinematic parameter is \(\epsilon\equiv 1-(\sum_i m_{\chi_i})/m_n\) [2112.09111][2212.04998]. A key model-building point is that with more than one \(\chi\) generation the decay width can scale as \(\epsilon^2\) rather than \(\epsilon^3\), which permits fitting the anomaly while suppressing crossed-process constraints such as \(\bar\chi n\to \chi\chi\) [2212.04998].

A further variant uses scalar leptoquarks as a portal to a dark scalar \(\phi\), producing the channel \(n\to \phi+\bar\nu\). In that model \(S_1^\alpha\) and \(S_1^\beta\) are scalar leptoquarks in the \((\bar 3,1,1/3)\) representation, \(\phi\) is a complex scalar with \(B=1\) and \(L=1\), and the effective hadronic coupling takes the form
\[
\mathcal{L}^{\rm eff}_{n\to \phi \bar\nu^i}
= \kappa_i\,\overline{n_L^C}\,\nu_L^i\,\phi^*+{\rm h.c.},
\]
with a benchmark \(m_\phi\simeq 938\) MeV and leptoquark masses near \(1.36\) TeV [2305.01727]. That construction is unusual in simultaneously targeting the neutron anomaly, freeze-in dark matter, muon \((g-2)\), and \(R_{D^{(*)}}\).

## 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 \((\psi_n,\psi_{n'})\) is related to the mass basis \((\psi_{n1},\psi_{n2})\) through
\[
\begin{pmatrix}\psi_n\\ \psi_{n'}\end{pmatrix}
=
\begin{pmatrix}
\cos\theta & \sin\theta\\
-\sin\theta & \cos\theta
\end{pmatrix}
\begin{pmatrix}\psi_{n1}\\ \psi_{n2}\end{pmatrix},
\]
and the vacuum oscillation probability is
\[
P_{n\to n'}(t)=\sin^2(2\theta)\,\sin^2\!\left(\frac{\Delta_{nn'}t}{2}\right)
\]
[2302.07805]. In traps, incoherent wall reflections reset the phase, so the oscillation channel becomes an effective disappearance rate,
\[
\lambda_{nn'}({\rm bottle})=\frac{1}{2\tau_f}\sin^2(2\theta),
\]
where \(\tau_f\) is the mean free-flight time. The same review argues that beam experiments are almost insensitive because
\[
P_{n\to n'}({\rm beam})\approx \frac{1}{2}\sin^2(2\theta)\sim 10^{-5},
\]
well below current beam precision [2302.07805].

The favored parameter region in that mirror-matter phenomenology is
\[
\sin^2(2\theta)\simeq (0.8\text{–}2)\times 10^{-5},\qquad
\Delta_{nn'}\simeq (3\text{–}11)\times 10^{-6}\ {\rm eV},
\]
which implies an intrinsic oscillation timescale of order ns and resonant magnetic fields
\[
B_{\rm res}\sim 50\text{–}200~{\rm T}
\]
[2302.07805]. 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 \(1\%\) beam bias to resonant conversion inside the \(4.6\) T NIST beam-lifetime solenoid. A dedicated SNS disappearance/regeneration search in a \(6.6\) T peak field found no signal, obtained \(p<2.5\times 10^{-8}\) at \(95\%\) CL, and excluded the full parameter band that would produce the required \((1.0\pm0.2)\%\) lifetime increase for \(\Delta m>10\) neV [2111.05543]. 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 \(n\to \chi+\gamma\), a Los Alamos search for monoenergetic \(\gamma\) rays ruled out this channel as the sole explanation of the anomaly with \(97\%\) CL [1905.01912]. For \(n\to \chi+e^+e^-\), UCNA obtained
\[
B<10^{-4}\quad (90\%~{\rm CL})
\]
for \(100~{\rm keV}<E_{e^+e^-}<644~{\rm keV}\), thereby excluding the channel as the sole explanation at the \(5\sigma\) level, while PERKEO II extended sensitivity to lower energies [1905.01912].

The PERKEO II reanalysis searched for a narrow line in the summed coincidence spectrum between \(0\) and \(644\) keV. At \(90\%\) CL it excluded a \(1\%\) branching fraction from \(32\) keV to the kinematic endpoint, covering \(95\%\) of the allowed \(\chi\)-mass range; at better than \(5\sigma\) local significance it excluded the \(1\%\) hypothesis from \(37.5\) keV to the endpoint, covering \(94\%\) of the allowed mass window [1905.01912]. The remaining low-energy corner survives mainly because the analysis required both detectors to trigger, which reduces acceptance for very low-\(Q\) events.

Other dark-decay realizations encounter orthogonal constraints. If the dark fermion is Majorana, two \(\Delta B=1\) insertions induce \(n\)-\(\bar n\) oscillations; in the explicit analysis of that scenario, the coupling needed for a \(1\%\) dark branching implies \(\tau_{n\bar n}\sim 10\) s, in violent conflict with the experimental lower limit \(\tau_{n\bar n}\gtrsim 10^8\) s [1804.09837]. By contrast, invisible \(n\to \chi\chi\chi\) models with \(N>1\) dark generations were constructed precisely so that matching \(\Delta\Gamma\) need not violate Kamiokande, SNO, and KamLAND neutron-disappearance bounds [2212.04998].

A broader phenomenological conclusion also emerges from global analyses based on the storage-method lifetime and precision \(g_A\): exotic neutron decays are bounded at
\[
<0.27\% \quad (95\%~{\rm CL}),
\]
which strongly disfavors any explanation that requires a full percent-level exotic branch unless the input value of \(g_A\) moves away from the most accurate measurements [1905.01912].

## 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 \(\chi\) in dense matter, the equation of state typically softens and the maximum mass falls below the observed \(2\,M_\odot\) scale. One route around this is repulsive dark matter–baryon cross-interactions. In a mean-field treatment with
\[
\epsilon(n_n,n_\chi)=\epsilon_{\rm nuc}(n_n)+\epsilon_\chi(n_\chi)+\frac{n_n n_\chi}{2z^2},
\]
the threshold for keeping stars nearly pure neutron matter is \(z\lesssim 71\) MeV for SLy-4 and \(m_n-m_\chi=1\) MeV [1811.06546]. A benchmark with \(m_\phi\approx0.1\) eV, \(g_n\approx -10^{-14}\), \(g_\chi\lesssim 4\times10^{-4}\), and \(z\approx 50\) MeV preserves \(M_{\max}\ge 2\,M_\odot\) [1811.06546].

A separate analysis of the Fornal–Grinstein channel \(n\to \chi+\phi\), using \(m_\phi=1\) MeV and \(m_\chi=937.7\) MeV, treats \(\chi\) as a self-interacting fermion gas and \(\phi\) as a trapped Bose-condensed boson. In that framework the neutron-star constraints require a repulsive \(\chi\)-\(\chi\) vector interaction of approximately
\[
G\approx 26~{\rm fm}^2
\]
to keep \(M_{\max}\ge 2\,M_\odot\), and the trapped boson must satisfy
\[
\tau_\phi > 1.85\times 10^{11}\ {\rm years}
\]
to avoid overheating old stars [2306.07509]. 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, \(m_\chi\approx 1\) GeV, \(g_\chi\approx 0.053\), and the full set of neutron-lifetime, relic-density, neutron-star, Higgs, and BBN constraints compresses the light scalar into the narrow interval
\[
2m_e < m_\phi < 2m_e + 0.0375~{\rm MeV}
\]
[2403.08666]. 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 \(m_\chi=938\) MeV and no explicit \(\chi\)-baryon portal, writing
\[
\mu_\chi=\sqrt{k_{F,\chi}^2+m_\chi^2}+G_v n_\chi
\]
for the dark fermion chemical potential [2505.09190]. In that analysis \(G_v=0\) softens the equation of state catastrophically and gives \(M_{\max}\approx0.7\,M_\odot\), whereas stiff and intermediate hadronic equations of state become viable for \(G_v\) of order \(10\)–\(100\ {\rm fm}^2\). Soft hadronic equations of state are effectively excluded once neutron-star and cluster self-scattering bounds are imposed [2505.09190].

The \(B_\chi=1/3\) scenario changes this logic because chemical equilibrium becomes \(\mu_\chi=\mu_n/3\) rather than \(\mu_\chi=\mu_n\). Both the effective-theory treatment and the explicit BSk24 analysis find that \(n\leftrightarrow \chi\chi\chi\) softens the neutron-star equation of state only mildly, so stars near \(2\,M_\odot\) remain allowed [2112.09111][2212.04998]. This difference is structural: the dense-matter cost of populating three light baryon-number-\(1/3\) 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,
\[
p+X\to H+X^+,
\]
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 [2003.02092][2011.13272]. In the detailed trap model,
\[
n_g=\frac{P}{k_B\sqrt{T_{\rm warm}T_{\rm cold}}},
\qquad
K_i=\int \sigma_{{\rm ce},i}(E)\,v(E)\,t_m\,P(E)\,dE,
\qquad
\epsilon = n_g\sum_i f_i K_i L_i,
\]
so the inferred beam lifetime shifts as
\[
\tau_{\rm beam}\approx \tau_n(1+\epsilon)
\]
for \(\epsilon\ll 1\) [2003.02092].

Using \(P=10^{-9}\) mbar, \(T_{\rm warm}=300\) K, \(T_{\rm cold}=4\) K, and a \(150^\circ\)C bakeout composition, one analysis finds
\[
\epsilon \approx 0.89\% \quad \Rightarrow \quad \Delta\tau \approx -7.8~{\rm s},
\]
with unbaked and \(400^\circ\)C-baked cases giving \(\epsilon\approx 1.8\%\) and \(1.1\%\), respectively [2003.02092]. A later reanalysis argues that an \(H_2\)-only residual gas, once the finite timing window is included, can still generate a \(\sim 3.4\) s downward correction; if the actual in-trap pressure were only \(2.6\) times the nominal warm reading, the correction would reach \(\sim 8.8\) s, i.e. essentially the full anomaly [2011.13272]. These papers also emphasize that elastic scattering at \(10^{-9}\) mbar is negligible and that dead-layer corrections alone would move the beam result upward, not downward [2003.02092][2011.13272].

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 \(n\)-\(\bar n\) 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 \(50\)–\(200\) T; and residual-gas charge exchange remains a quantitatively testable beam-systematic alternative [1905.01912][2111.05543][2302.07805][2003.02092]. 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.

Source: https://www.emergentmind.com/topics/neutron-decay-anomaly-model