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Neutron Decay Anomaly and Its Effects on Neutron Star Properties

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper argues that neutron-star observations can place joint constraints on the self-interaction strength of dark matter produced by the neutron decay anomaly, and that the combination of pulsar masses, NICER radii, GW170817 tidal…

desk verdict A competent EOS paper whose central constraints hinge on a misread cluster bound; worth a careful revision, not a desk reject. read the letter →

arxiv 2505.09190 v1 pith:6YEEPF7G submitted 2025-05-14 astro-ph.HE nucl-th

H. C. Das , G. F. Burgio This is my paper · ORCID
classification astro-ph.HEnucl-th
keywords neutrondecayanomalydarkmatterstarequationofstateself-interactingtidaldeformabilityrelativisticmean-fieldfraction
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that neutron stars can act as laboratories for the neutron decay anomaly, the unresolved roughly nine-second discrepancy between bottle and beam measurements of the neutron lifetime. If a small fraction of neutrons decays into a dark fermion plus a light boson, then inside a neutron star the decay products form a degenerate dark-matter component whose self-interaction strength is a single parameter $G_v$. Building three new relativistic mean-field equations of state (HCD0\textendash HCD2) and varying $G_v$, the paper shows that pulsar mass, NICER radius, GW170817 tidal-deformability, and galaxy-cluster self-scattering limits jointly constrain $G_v$. The result is that cluster data give a lower bound $G_v = 4.25\,\mathrm{fm^2}$, the two-solar-mass pulsar demands larger model-dependent lower bounds (from 8.74 to 250.90 $\mathrm{fm^2}$), and the softest hadronic model is excluded. In this scenario, a maximum-mass neutron star can contain at most about 39\% dark matter by mass.

What carries the argument

The load-bearing object is the dark fermion $\chi$ produced by $n\to\chi+\phi$ inside neutron stars, treated as a degenerate Fermi gas with a repulsive vector self-interaction. Its energy density and chemical potential include a term proportional to $G_v=(g_v/m_v)^2$, and chemical equilibrium with neutrons, $\mu_\chi=\mu_n$, fixes the dark-matter fraction. The transfer from galaxy-cluster observations to the neutron-star parameter is the zero-velocity Born-approximation cross-section $\sigma/m_\chi \simeq 0.59\times10^{-2}(G_v/\mathrm{fm^2})^2(m_\chi/\mathrm{GeV})\,\mathrm{cm^2/g}$, which converts $\sigma/m_\chi=0.1\,\mathrm{cm^2/g}$ into $G_v=4.25\,\mathrm{fm^2}$. These pieces make the dark-matter concentration a function of one tunable parameter, so every neutron-star observable responds predictably as $G_v$ varies.

What would settle it

Measure the self-scattering cross-section of the decay-produced dark fermion at neutron-star-typical densities and momenta, or detect a $2\,M_\odot$ neutron star with an independently inferred dark-matter fraction above about 39\%, either of which would contradict the paper's central bound and its exclusion of the softest equation of state.

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Extended reading notes

Core claim

The central claim is that a single parameter, the vector self-coupling $G_v=(g_v/m_v)^2$, controls how much of a neutron star's interior becomes dark matter in the $n\to\chi+\phi$ decay channel. Fixing the dark fermion mass at 938 MeV and imposing chemical equilibrium $\mu_\chi=\mu_n$, the dark-matter fraction $f_\chi$ is determined by $G_v$: small $G_v$ means abundant dark matter, a softened equation of state, and a reduced maximum mass, while large $G_v$ suppresses the dark component. Combining the observed two-solar-mass pulsar, NICER radii, the GW170817 tidal-deformability limit, and the galaxy-cluster self-interaction bound $\sigma/m_\chi=0.1\,\mathrm{cm^2/g}$, the paper derives lower bounds on $G_v$ that vary with the hadronic model and finds that the softest model, HCD2, cannot satisfy both the mass and the cluster constraints simultaneously.

Load-bearing premise

The argument assumes that the self-scattering cross-section measured in galaxy clusters, where dark matter moves at roughly a thousand kilometres per second, can be converted by a low-velocity Born formula into the self-interaction strength of the dense, relativistic dark matter inside a neutron star; if the scattering depends on velocity or the two populations are different species, the $G_v$ bounds do not follow.

Editorial extensions

If this is right

  • If the model is correct, a two-solar-mass neutron star requires $G_v$ above roughly $8.74\,\mathrm{fm^2}$ for the stiffest equation of state and as high as $250.9\,\mathrm{fm^2}$ for the softest, capping the dark-matter fraction at maximum mass near 27\% when only pulsar masses are used.
  • Combining galaxy-cluster scattering data with the pulsar-mass limit narrows the allowed window for $G_v$ to roughly $8.74\text{--}134.4\,\mathrm{fm^2}$ for the stiffest models and excludes the softest hadronic equation of state, HCD2.
  • A dark-matter-admixed neutron star has a smaller radius and smaller tidal deformability than a purely hadronic star of the same mass; for HCD0, $\Lambda_{1.4}$ drops from about 749 to about 436 at $G_v=10\,\mathrm{fm^2}$, so future mass-radius and gravitational-wave measurements can probe the dark-matter fraction.
  • Cluster data alone limit the dark-matter fraction inside a maximum-mass star to at most about 39\% by mass, meaning that a neutron star in this scenario cannot be mostly dark matter.
  • Dedicated Bayesian or machine-learning analyses of combined pulsar, NICER, and GW data could turn the qualitative $G_v$ boundaries into precise posterior constraints on the dark-matter self-interaction strength.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Future neutron-star cooling or r-mode measurements could test the predicted dark-matter fraction of roughly 1\textendash 39\%: a degenerate dark core of that size would alter the specific heat and damping times in ways that are partially separable from hadronic uncertainties.
  • The same Born-approximation conversion maps other self-interacting dark-matter candidates onto neutron-star observables; if future halo measurements show strong velocity dependence in $\sigma/m_\chi$, the simple $G_v$ bounds and the exclusion of the softest equation of state would need revision.
  • A multi-messenger fit combining a second gravitational-wave tidal-deformability event with more NICER-like radius measurements could sharpen the paper's qualitative exclusion of HCD2 into quantitative posterior probabilities on $G_v$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript studies the neutron decay anomaly (NDA) as a source of dark matter inside neutron stars. Within a relativistic mean-field (RMF) framework, the authors construct three hadronic equations of state (HCD0-HCD2) that satisfy current neutron star mass, radius, and tidal deformability constraints, then add a degenerate dark fermion gas (m_chi = 938 MeV) produced via n -> chi + phi, with a vector self-interaction parametrized by Gv. Solving the beta-equilibrium, charge neutrality, and TOV equations, they compute mass-radius relations, tidal deformabilities, and dark matter fractions as functions of Gv. Combining neutron star observations (PSR J0740+6620 mass, NICER radii, GW170817 tidal deformability) with galaxy cluster self-interaction cross-section limits, they derive model-dependent lower bounds on Gv (8.74, 21.88, and 250.90 fm^2 for HCD0-2 from the 2 M_sun constraint), report a galaxy-cluster lower bound of Gv = 4.25 fm^2, and use an upper bound Gv <= 134.4 fm^2 from the core-cusp problem to conclude that the softest model HCD2 is excluded and that the dark matter fraction is at most about 39% for stiff equations of state.

Significance. If the cluster-to-Gv conversion were robust, the paper would provide a useful cross-domain constraint connecting the neutron lifetime anomaly to dark matter self-interactions in halos and stars. The systematic scan over Gv across eight RMF models and the construction of the HCD family are strengths, and the TOV/EOS machinery follows established practice. The main significance lies in the idea of combining pulsar masses, NICER radii, GW170817, and cluster cross-section limits to jointly bound the self-interaction parameter. However, the quantitative claims currently rest on an insecure mapping between cluster cross-sections and the in-star self-interaction, and in one case on a reversed inequality direction; these issues affect the central conclusions rather than only the presentation.

major comments (3)
  1. [Sec. 3.5, Eqs. (10)-(12)] The paper treats sigma/m_chi = 0.1 cm^2/g from galaxy clusters as a lower bound on Gv (Gv = 4.25 fm^2), but the cluster observations cited in Refs. [64-66] generally report upper limits on the self-interaction cross-section. With an upper limit, Eq. (12) yields Gv <= 4.25 fm^2, which conflicts with the 2 M_sun lower bounds (e.g., Gv >= 8.74 fm^2 for HCD0). The claimed combined allowed region, the f_chi <= 39% upper bound, and the HCD2 exclusion all depend on this directionality; the authors must either justify that 0.1 cm^2/g is a measured lower limit or revise the conclusions.
  2. [Sec. 3.5, Eq. (10)] The cluster-to-Gv conversion uses the low-velocity Born approximation, appropriate for halo dark matter with velocities of order 10^3 km/s. Inside the neutron star the dark fermions are degenerate, with Fermi momenta reaching several hundred MeV for the densities shown in Fig. 2, so the scattering is neither low-velocity nor in the Born regime for the large Gv values considered (up to a few hundred fm^2). The same Gv therefore does not lead to a scale-independent sigma/m_chi, and the derived bounds of 4.25, 13.44, and 134.4 fm^2 do not directly apply to the in-star self-interaction. A velocity-dependent treatment of the transfer cross-section is required before these constraints can be used.
  3. [Sec. 3.5, 'core-cusp problem' line] The paper uses sigma/m_chi <= 100 cm^2/g to set Gv <= 134.4 fm^2 and thereby exclude HCD2, which requires Gv > 250.9 fm^2. The core-cusp problem is generally used to motivate a lower bound on the self-interaction cross-section at dwarf-galaxy scales, not an upper bound at the level of 100 cm^2/g; standard cluster upper limits are at the level of about 1 cm^2/g. The stated upper bound therefore does not follow from the cited constraints, and the exclusion of HCD2 is not supported unless a specific, valid upper limit is identified.
minor comments (5)
  1. [Eq. (10)] The equation contains a duplicated final line ('sigma approx 2.5 x 10^-21 ... cm^2' appears twice); please remove the repetition.
  2. [Fig. 4 caption] The caption lists markers as 'the markers ,■ and⋆', but one marker glyph is missing in the typeset text; the symbols should be printed or described explicitly.
  3. [Sec. 2.2] The paper fixes m_chi = 938 MeV but does not state the dark-boson mass m_phi; since the decay n -> chi + phi must be kinematically allowed, a sentence specifying the allowed range of m_phi would be helpful.
  4. [Sec. 3.5] The factor-of-100 difference between Eq. (10) and Refs. [62,63] is addressed only in a footnote; because this factor directly affects all cluster-derived limits, the derivation should be presented more transparently in the main text.
  5. [Sec. 3.4] The text notes that HCD2 'just touches the lower value of PSR J0740+6620' and later reports a 2 M_sun lower bound of 250.90 fm^2 for HCD2; a short explanation of the steep sensitivity of the lower bound to the EOS stiffness would help the reader interpret the model dependence.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the G_v and dark-matter-fraction constraints are derived from external neutron-star and galaxy-cluster observations, not from the model inputs.

full rationale

The paper's central quantitative claims are the lower/upper bounds on the self-interaction parameter G_v and the associated dark-matter fractions. These are obtained by combining the model EOS with externally measured inputs: PSR J0740+6620 mass, NICER radii, GW170817 tidal deformability, and galaxy-cluster self-scattering cross-section limits. The mapping from sigma/m_chi to G_v in Eqs. (10)-(12) is an algebraic conversion of an external observable, not a renaming of an input assumption of the neutron-decay model. The dark-matter fraction f_chi is then an output of solving the beta-equilibrium and TOV equations, not a fitted quantity. The HCD models are admittedly constructed to satisfy the very astrophysical constraints they are later checked against, and the paper states this explicitly: 'we developed three models named HCD0, HCD1, and HCD2 for different values of zeta0, which satisfy the constraint of the NS maximum mass >= 2 M_sun'. This is calibration rather than prediction, and it does not force the G_v-dependent behavior, which is the actual novel content. The galaxy-cluster limit is used to exclude HCD2 logically: HCD2 requires G_v >= 250.90 fm^2 to reach 2 M_sun, while the cluster-informed upper bound is G_v <= 134.4 fm^2. Even if the interpretation of the cluster bound as a lower versus upper limit is physically debatable, that is a correctness or assumption risk, not circularity. Self-citations appear for saturation properties and previously published EOSs, but the load-bearing steps do not reduce to those citations. No equation is defined in terms of the quantity it is alleged to predict, and no fitted parameter is relabeled as a prediction. The derivation chain is therefore self-contained with respect to circularity, with the caveat that the external validity of the cluster-to-star mapping is an astrophysical assumption rather than a logical tautology.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central calculation rests on the RMF model of nuclear matter, the neutron decay anomaly scenario, the neglect of DM-baryon interactions, the Born-approximation mapping from galaxy cluster cross-sections to Gv, and the observational inputs treated as hard constraints. The only free parameter explicitly tuned in this paper is zeta0, which is set to satisfy the 2 Msun constraint for each model; Gv and m_chi are model parameters inherited from the dark matter model.

free parameters (3)
  • zeta0 (omega meson self-interaction coupling) = HCD0: 0, HCD1: 1.4225, HCD2: 2.9216
    Tuned by hand in Sec 3.1 to produce stiff, intermediate, and soft EOSs with maximum masses 2.52, 2.19, and 2.02 Msun, respectively, specifically to satisfy the 2 Msun pulsar constraint.
  • Gv (dark matter self-interaction strength, (g_v/m_v)^2) = scanned from 1e-4 to 1e4 fm^2; constrained to >= 4.25 fm^2 by galaxy clusters and >= 8.74 to 250.9 fm^2 by NS…
    The central free parameter of the DM model (Sec 2.2); the paper's claims are about its allowed range.
  • m_chi (dark fermion mass) = 938 MeV
    Chosen by hand following Refs. [10,33] in Sec 2.2; not fitted in this paper, but results depend on it.
assumptions (5)
  • domain assumption The relativistic mean-field Lagrangian (Eq. 1) with the given meson couplings and the mean-field approximation describes nuclear matter accurately up to neutron star densities.
    Standard model in dense-matter physics; the authors use it without re-derivation.
  • domain assumption The neutron decay anomaly model holds: a fraction of neutrons decay into a dark fermion chi (mass 938 MeV) and a light boson phi, and in neutron stars chi reaches chemical equilibrium with neutrons (mu_chi = mu_n in Eq. 8).
    This is the physical scenario under investigation, adopted from Refs. [3,10,33].
  • domain assumption DM-baryon interactions are negligible for the EOS and stability of the admixed star.
    Explicitly stated in Sec 2.2 as a simplification to be addressed in future work; strong DM-baryon coupling would change the DM fraction and all derived bounds.
  • domain assumption The low-velocity Born approximation cross-section (Eq. 10) and the conversion sigma/m_chi -> Gv (Eq. 11) apply to the in-situ dark matter inside neutron stars.
    The galaxy cluster bounds are velocity-dependent and derived at halo velocities, but the neutron star dark matter is degenerate and relativistic; this mapping is used without discussion of its regime of validity.
  • domain assumption The observational inputs (PSR J0740+6620 mass, NICER radii, GW170817 tidal deformability, galaxy cluster cross-sections) are correct and can be treated as hard constraints without propagating their uncertainties.
    The paper overlays deterministic curves on observational contours and reports bounds as exact numbers.

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Pith. "Pith review of Neutron Decay Anomaly and Its Effects on Neutron Star Properties." pith.science (2026). https://pith.science/paper/6YEEPF7G

@misc{pith2026250509190,
  author       = {Pith},
  title        = {Pith review of: Neutron Decay Anomaly and Its Effects on Neutron Star Properties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6YEEPF7G}},
  note         = {Machine review of arXiv:2505.09190}
}
abstract

We investigate the effects of dark matter (DM) on neutron star (NS) properties using the neutron decay anomaly model within the relativistic mean-field (RMF) framework. Three nucleonic models (HCD0-HCD2) are developed, satisfying astrophysical constraints such as the maximum NS mass ($\geq 2 M_\odot$), the NICER mass-radius limits, and the tidal deformability constraint from the GW170817 event. The equation of states of the NS admixed with DM (DMANS) are calculated by incorporating the self-interactions between them. The macroscopic properties, such as mass, radius, and tidal deformability of the NSs, are obtained for HCD models along with five others by varying self-interaction strength. By combining NS observations with scattering cross-section constraints from galaxy clusters, we explore model-dependent trends in the DM self-interaction parameter space. While the quantitative bounds may vary with hadronic model choice, our analysis offers insights into the interplay between DM interactions and NS observables within the RMF framework.

Figures

Figures reproduced from arXiv: 2505.09190 by the authors.

Figure 1
Figure 1. EOSs(left), M − R relations (middle), and tidal deformability (right) are shown for HCD0-2 models. The marker represents the value corresponding to the maximum mass cases. The contours of 68 and 95 % are from three separate NICER observations for different pulsars [46,47,49]. The horizontal fill band represents the maximum mass constraints from Fonseca et al. [50] for PSR J0740+6620. In [PITH_FULL_IMAGE:figures/ful… view at source ↗
Figure 2
Figure 2. Particle fractions for all species, including DM, are shown as a function of baryon density for the HCD0 model. The shaded areas are calculated for different Gv values in the range 0 − 300 fm2 . The dashed colored lines represent the composition inside the NSs without DM. The vertical arrow represents the trend of the neutron population with increasing Gv values. 2 fm−3 . The obtained PFs for the different species a… view at source ↗
Figure 3
Figure 3. EOSs (left), M − R relations (central), and tidal deformability (right) panels are shown for three models HCD0-2 by varying Gv values, ranging from 10 to 300 fm2 . The horizontal filled band represents the maximum mass constraints from Fonseca et al. [50] for PSR J0740+6620. The contours of 68 and 95 % are from three separate NICER observations for different pulsars as mentioned in the legend [46,47,49]. value of Λ1… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Maximum mass (Mmax), radius corresponds to Mmax/1.4, and canonical tidal deformability are shown as a function of Gv. Solid and dashed lines are for different observations. Similarly, the markers , ■ and ⋆ represent the lower bound of Gv obeying different observational…
Figure 5
Figure 5. Figure 5: DM fractions with different values of Gv using Eq. (10). Markers and ⋆ represent the lower bound of Gv satisfying the 2M⊙ constraint and Galaxy cluster limit, respectively. The fill areas (red, blue, and rust) represent the values of Gv for which different models achie…

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