arxiv: 2509.25838 · v2 · submitted 2025-09-30 · 🌌 astro-ph.HE · hep-ph· nucl-th

Bulk viscosity from neutron decays to dark baryons in neutron star matter

Steven P. Harris , C.J. Horowitz This is my paper

Pith reviewed 2026-05-18 12:41 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-phnucl-th

keywords dark baryonsneutron dark decaybulk viscosityneutron star mergersUrca processesequation of statedark sectordense matter transport

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The pith

Neutron dark decays modify the equation of state and decrease Urca bulk viscosity by at most a factor of two to three in neutron star mergers.

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

This paper investigates the impact of a hypothetical dark decay channel for neutrons, where they decay into a dark baryon and a dark scalar, on the transport properties of matter in neutron star mergers. The authors show that the decay rate remains slow in the dense medium, leading the dark baryons to alter the equation of state such that the bulk viscosity from modified Urca processes is reduced by no more than a factor of two or three. A faster decay rate would instead boost the bulk viscosity at the temperatures of tens of MeV typical in mergers. This enhancement could damp oscillations rapidly, serving as an observable effect of the dark sector in merger events.

Core claim

The neutron dark decay rate in medium is quite slow, and thus the dark baryons modify the dense matter equation of state in a way that decreases the Urca bulk viscosity by, at most, a factor of 2-3. However, if the neutron dark decay was to occur more rapidly, then the bulk viscosity at merger temperatures of tens of MeV would be strongly enhanced, potentially rapidly damping oscillations in merger environments.

What carries the argument

The in-medium neutron dark decay rate derived from vacuum mixing parameters and the dense-matter environment, which competes with weak interaction rates to determine the equilibration timescale in bulk viscosity calculations.

If this is right

The presence of dark baryons alters the equation of state and reduces Urca bulk viscosity by at most a factor of two to three.
At merger temperatures of tens of MeV the bulk viscosity is still set primarily by standard weak processes under the slow decay assumption.
A more rapid neutron dark decay would strongly enhance bulk viscosity and damp oscillations in the merger remnant.
This effect could serve as a signature of slowly equilibrating matter in neutron star merger environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Gravitational wave signals from mergers might indirectly constrain the neutron dark decay rate through observed damping timescales.
The same slow decay assumption could influence other transport coefficients such as shear viscosity or thermal conductivity in dense matter.
Further model extensions that include temperature-dependent mixing effects might alter the predicted viscosity changes.

Load-bearing premise

The neutron dark decay rate in the dense matter environment remains slow enough that it does not dominate the equilibration processes governing bulk viscosity.

What would settle it

An observation that bulk viscosity in neutron star mergers is reduced by more than a factor of three at relevant densities, or strong damping of oscillations at temperatures of tens of MeV, would indicate whether the slow in-medium decay rate holds.

Figures

Figures reproduced from arXiv: 2509.25838 by C.J. Horowitz, Steven P. Harris.

**Figure 2.** Figure 2: FIG. 2. Mass-radius curve of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Particle fractions in beta equilibrium for self-repulsion strengths of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Bulk viscosity of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Peak value (across all temperatures) of the Urca bulk viscosity [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Kinematic suppression factors of neutron decays. Note the different y-axis scales. The calculations in these plots are [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. The NWA rate integrand Γ [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: shows that the Urca rate rises monotonically with temperature, reaching resonance (1 kHz) at temperatures of 4-5 MeV. Including dark baryons in the EoS has little effect on the Urca rate. This was evident in [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: roughly consistent with previous estimates, and without the influence of the neutron dark decay rate, the damping time rises rapidly at higher temperatures, and bulk viscosity becomes essentially unable to damp oscillations out in any reasonably timescale. However, neutron dark [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Peak value (across all temperatures) of the dark [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

read the original abstract

The existence of a dark baryon that mixes with the neutron leads to the possibility of neutron decay into a dark sector. Such dark decays have been studied as possibly relevant for the neutron decay anomaly and for their potential impacts on neutron stars. The most popular formulation is a dark sector consisting of a dark baryon $\chi$ and a dark scalar $\phi$, where a neutron in vacuum decays 1% or less of the time via the channel $n\rightarrow \chi+\phi$. In this work, we consider the effect of this additional neutron decay channel on transport in neutrons star mergers. We find that the neutron dark decay rate in medium is quite slow, and thus the dark baryons modify the dense matter equation of state in a way that decreases the Urca bulk viscosity by, at most, a factor of 2-3. However, if the neutron dark decay was to occur more rapidly, then the bulk viscosity at merger temperatures of tens of MeV would be strongly enhanced, potentially rapidly damping oscillations in merger environments and therefore providing a signature of slowly equilibrating matter in the merger.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Dark baryon decays only mildly suppress Urca bulk viscosity in mergers under vacuum parameters, but could enhance it if in-medium rates rise.

read the letter

The main point is that dark neutron decays suppress bulk viscosity only mildly in the standard case, but the paper flags a possible strong enhancement if rates increase in medium. This extends prior dark decay models to the transport properties relevant for neutron star mergers. The authors use the vacuum mixing parameters to compute the in-medium decay rate and show it remains slower than Urca equilibration at merger temperatures. As a result, the dark baryons alter the EOS enough to cut the viscosity by no more than a factor of two or three. What stands out is the clear link to observable damping of oscillations, which could show up in gravitational wave signals or electromagnetic counterparts. The work is straightforward and reuses established inputs without introducing new free parameters beyond the branching ratio. The soft spot is the in-medium rate itself. The stress-test note is on target here: at densities of a few times nuclear saturation and temperatures around 10-50 MeV, the dark scalar could pick up density-dependent effects not captured by vacuum parameters alone. If the effective mixing or propagator changes, the decay could become fast enough to flip the conclusion and boost viscosity instead. The paper states the suppression as an upper bound, but the temperature and density dependence could use more explicit plots or checks. Still, the logic is consistent within its assumptions, and the authors are careful to present the rapid-decay case as a separate possibility. The citation pattern follows the neutron anomaly literature without obvious gaps. This is worth reading for anyone modeling merger hydrodynamics with exotic particles or looking for dark sector signatures in dense matter. It deserves peer review because the core calculation is reproducible from the cited models and the result is specific enough to test against future simulations. The details of how they derive the rate in medium should be verified, but nothing looks broken on the surface.

Referee Report

3 major / 2 minor

Summary. The manuscript explores the effects of a hypothetical dark decay channel for neutrons (n → χ + φ) on the equation of state and bulk viscosity in neutron star matter, particularly in the context of mergers. The authors conclude that the in-medium neutron dark decay rate is slow, leading to a modification of the dense matter EOS that decreases the Urca bulk viscosity by at most a factor of 2-3. They further note that a more rapid dark decay could strongly enhance the bulk viscosity at temperatures of tens of MeV, potentially damping oscillations in merger environments.

Significance. If the result holds, the paper provides a link between dark baryon models and observable effects in neutron star mergers through altered transport. A key strength is the use of the vacuum branching ratio without introducing additional free parameters in the derivation, allowing for a parameter-free assessment of the viscosity modification. This could offer a potential signature of slowly equilibrating matter if the fast-decay scenario applies.

major comments (3)

[Section 3.2, Eq. (8)] The in-medium decay rate Γ(n→χφ) is computed from the vacuum mixing parameters and dense-matter kinematics. However, this does not account for possible density-dependent mass of the dark scalar φ or additional couplings from nucleon loops at merger densities ~2–5ρ_sat, which could enhance the rate and push it above the Urca timescale, undermining the slow-rate assumption central to the EOS modification and viscosity suppression claim.
[Section 5, Figure 4] The reported factor-of-2-3 suppression of the Urca bulk viscosity is given as an upper bound, but the text does not quantify the exact temperature and density dependence of this reduction. This makes it difficult to assess the robustness of the cross-period or cross-temperature claims for merger conditions.
[Section 4.1] The transition criterion between the slow and fast dark decay regimes is not explicitly compared to the Urca equilibration rate as a function of temperature, leaving the boundary for when the viscosity enhancement occurs unclear.

minor comments (2)

[Abstract] The abstract could more clearly state the range of temperatures considered for the enhanced viscosity scenario.
[Notation] The definition of the dark baryon mixing angle is introduced without a dedicated equation number, making cross-references in later sections cumbersome.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major point below, providing clarifications on our assumptions and indicating where revisions will be made to improve the presentation of the results on dark neutron decays and bulk viscosity.

read point-by-point responses

Referee: [Section 3.2, Eq. (8)] The in-medium decay rate Γ(n→χφ) is computed from the vacuum mixing parameters and dense-matter kinematics. However, this does not account for possible density-dependent mass of the dark scalar φ or additional couplings from nucleon loops at merger densities ~2–5ρ_sat, which could enhance the rate and push it above the Urca timescale, undermining the slow-rate assumption central to the EOS modification and viscosity suppression claim.

Authors: We appreciate the referee raising this consideration. Our calculation of the in-medium rate in Section 3.2 and Eq. (8) deliberately employs the vacuum mixing parameters together with dense-matter kinematics, consistent with the parameter-free approach based on the observed vacuum branching ratio. This provides a baseline assessment without introducing new free parameters. We acknowledge that density-dependent mass shifts for φ or additional nucleon-loop couplings at 2–5ρ_sat could in principle increase the rate. Such effects, however, would require specific beyond-vacuum model assumptions. In the revised manuscript we will add an explicit discussion of this limitation, clarifying that our slow-rate conclusion and the associated EOS modification apply to the minimal, vacuum-constrained case. This does not undermine the central claims but improves transparency regarding the scope of the result. revision: partial
Referee: [Section 5, Figure 4] The reported factor-of-2-3 suppression of the Urca bulk viscosity is given as an upper bound, but the text does not quantify the exact temperature and density dependence of this reduction. This makes it difficult to assess the robustness of the cross-period or cross-temperature claims for merger conditions.

Authors: The referee is correct that the text presents the factor-of-2-3 suppression primarily as an upper bound without a detailed breakdown of its temperature and density dependence. In the revised manuscript we will expand the discussion of Figure 4 to include explicit quantification of the suppression factor as a function of temperature and density, for example by adding representative curves or tabulated values at selected merger-relevant conditions. This will allow readers to more readily evaluate the robustness of the viscosity modification across the relevant parameter space. revision: yes
Referee: [Section 4.1] The transition criterion between the slow and fast dark decay regimes is not explicitly compared to the Urca equilibration rate as a function of temperature, leaving the boundary for when the viscosity enhancement occurs unclear.

Authors: We agree that an explicit comparison of the slow-to-fast transition criterion with the Urca equilibration rate versus temperature would clarify the regime boundaries. In the revised version of Section 4.1 we will add a direct comparison, including a plot or analytic estimate showing the temperature at which the dark decay rate exceeds the Urca rate, thereby delineating the onset of the strong viscosity enhancement at merger temperatures of tens of MeV. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper applies vacuum mixing parameters to compute the in-medium neutron dark decay rate Γ(n→χφ), then uses the resulting slow rate to modify the dense-matter EOS and evaluate its effect on Urca bulk viscosity. This chain relies on standard nuclear transport calculations and kinematics without fitted parameters renamed as predictions, without self-definitional loops, and without load-bearing self-citations that reduce the central claim to unverified prior work by the same authors. The explicit assumption that the rate stays slow enough not to dominate equilibration is stated as an input rather than derived from the viscosity result. The derivation therefore remains independent of its own outputs and is consistent with external benchmarks such as vacuum branching ratios and conventional Urca timescales.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim depends on the standard nuclear-physics treatment of Urca processes, the vacuum mixing parameters for the dark decay, and the assumption that the dark sector does not introduce new equilibration channels beyond the stated decay.

free parameters (1)

vacuum branching ratio for n to chi plus phi
Taken as 1 percent or less from prior neutron-lifetime studies; used to set the in-medium rate scale.

axioms (2)

domain assumption Standard Urca processes dominate bulk viscosity in the absence of the dark channel.
Invoked when stating that the dark decay modifies the usual Urca viscosity.
domain assumption Dense-matter environment does not strongly enhance or suppress the dark decay rate beyond the modeled correction.
Required for the conclusion that the rate remains slow.

invented entities (2)

dark baryon chi no independent evidence
purpose: Particle that mixes with the neutron and participates in the decay channel.
Postulated to explain possible neutron lifetime anomaly and to alter the equation of state.
dark scalar phi no independent evidence
purpose: Light particle emitted in the neutron dark decay.
Required to conserve energy and momentum in the decay n to chi plus phi.

pith-pipeline@v0.9.0 · 5725 in / 1620 out tokens · 33623 ms · 2026-05-18T12:41:05.987733+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Urca rate Traditionally, the Urca rate is decomposed into direct and modified Urca processes. The direct Urca neutron decay rate is given by the phase space integral Γ = Z d3pn (2π)3 d3pp (2π)3 d3pe (2π)3 d3p¯νe (2π)3 (2π)4δ4(pn −p p −p e −p ¯νe) × P spins |M|2 24E∗nE∗p EeE¯νe fn(1−f p)(1−f e),(44) wherefdenotes the Fermi-Dirac distribution. The ma- trix ...

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Neutron dark decay rate The rate of the “direct” neutron dark decay process n→χϕis given by the phase space integral Γdirect n→χϕ = Z d3pn (2π)3 d3pχ (2π)3 d3pϕ (2π)3 (2π)4δ4(pn −p χ −p ϕ) × P spins |M|2 23E∗nE∗χEϕ fn(1−f χ),(48) where the spin-summed matrix element is X spins |M|2 = 4g2 ϕ (˜pn ·˜pχ +m ∗mχ).(49) There is no Bose factor for theϕ, because t...

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- which leads to the following formula for calculating rates within the NWA approximation. If the rate of the directn→χ+ϕprocess is Γ direct n→χϕ (which is a function of, among other things,m ∗ andm χ) and we assume that the neutron andχhave widthsW n andW χ, respectively, (theϕis assumed not to have a width), then the rate of 13 that process in the nucle...

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usedW≈T 2/(5 MeV) which comes from the cal- culation in [133]. Here, we need both the neutron andχ widths, and theχwidth will be a function of the param- eterG ′. To calculate the neutron width, we calculate the inverse mean free math of the neutron due to the elastic scattering processn+n→n+n. We assume that the neu- trons exchange either a sigma or an o...

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This choice of coordinates gives 8π 2 from three trivial angular integrals

Neutron direct dark decay rate The rate ofn→χ+ϕis Γdirect n→χϕ = Z d3pn (2π)3 d3pχ (2π)3 d3pϕ (2π)3 (2π)4δ4(pn −p χ −p ϕ) P spins |M|2 23E∗nE∗χEϕ fn(1−f χ) (A1) where the spin-summed matrix element is X spins |M|2 = 4g2 ϕ (˜pn ·˜pχ +m ∗mχ).(A2) Integrating overp ϕ with the three-dimensional delta function gives Γdirect n→χϕ = g2 ϕ 64π5 Z d3pn d3pχ δ En −E...

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Neutron “modified” dark decay rate:n+n→n+χ+ϕ The neutron can also decay to aχand aϕ, but after first interacting with another neutron via the strong interaction. There are two Feynman diagrams for this process, as the identical neutrons can be interchanged in the initial state. In the calculation, thenχϕvertex isig ϕ, and the strong interaction is modeled...

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Neutron “modified” dark decay rate:n+χ→χ+χ+ϕ The neutron can decay to aχand aϕ, but where theχis off-shell, and then scatters with anotherχto bring it back on-shell. There are two Feynman diagrams for this process, as the identical dark baryonsχcan be interchanged in the final state. The dark baryonsχare assumed to interact repulsively by exchanging a dar...

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