Density-induced dark-baryon conversion in $Δ-$admixed hypernuclear neutron stars

Abstract: We investigate density-induced conversion of neutrons into a neutral dark baryon $χ$ in cold, charge-neutral, $β$-equilibrated neutron-star matter containing hyperons and all $Δ(1232)$ quartet. The hadronic sector is modeled within a density-dependent covariant density-functional framework using the DDME2 parametrization. A scalar Higgs portal is included as a possible interaction channel between the visible and dark sectors, although its mean-field contribution is negligible for the couplings adopted here. Unlike fixed dark-matter admixture models or scenarios in which nucleon-to-DM conversion is driven by Higgs exchange, the $χ$ abundance is determined self-consistently from chemical equilibrium and baryon-number conservation. We find that hyperons and $Δ$ resonances alter the neutron chemical potential, delay the onset of $χ$, and suppress its abundance relative to nucleonic matter. This competition induces characteristic changes in the equation of state, particle fractions, sound speed, and adiabatic index. For $m_χ=1250$, $1300$, and $1400$ MeV, the maximum masses of the complete $N+Y+Δ+χ$ configurations are $1.806$, $1.899$, and $2.024,M_\odot$, respectively, indicating that the massive-pulsar constraint disfavors the lighter dark-baryon benchmarks. The radial profiles further show that for $m_χ=1400$ MeV, $χ$ is confined to the inner core of the most massive stars, while canonical configurations remain essentially unaffected. Thus, the stellar modifications arise primarily from conversion-induced rearrangement of the equilibrium composition rather than from Higgs-mediated interactions. These results highlight the importance of treating conventional non-nucleonic degrees of freedom and density-generated dark baryons on an equal footing when assessing the astrophysical viability of dark-sector extensions of dense matter.

• The paper demonstrates that self-consistent chemical equilibrium between neutrons and dark baryons delays conversion until roughly 3.5–4.3 times nuclear saturation density when hyperons and Δ resonances are included.
• The results show that dark-baryon conversion softens the equation of state and reduces the maximum mass, with only dark-baryon masses near 1.38–1.40 GeV supporting approximately 2-solar-mass neutron stars in the adopted model.
• The study finds that canonical 1.4-solar-mass stars remain largely insensitive to dark-baryon formation, while sufficiently massive stars can develop compact dark cores and exhibit reduced sound speeds near particle thresholds.

Motivation and scope

This paper investigates the in-medium conversion of neutrons into a neutral, baryon-number-carrying dark-sector fermion $\chi$ in cold, charge-neutral, $\beta$-equilibrated neutron-star (NS) matter that also contains hyperons and the complete $\Delta(1232)$ quartet. The hadronic sector is treated within a density-dependent covariant density-functional (CDF) framework using the DDME2 parameterization [2005PhRvC..71b4312L], extended to the baryon octet and $\Delta$ resonances following earlier work by the same collaboration [Thapa_2021, Parmar_2025]. The central methodological distinction from most dark-matter-admixed NS studies is that the dark-baryon abundance is not prescribed as a fixed mass fraction or Fermi momentum; instead, it is determined self-consistently from chemical equilibrium ($\mu_n = \mu_\chi$), total baryon-number conservation, charge neutrality, and weak equilibrium, with an onset condition $\mu_n \geq m_\chi^*$ analogous to threshold conditions for hyperon appearance. The mechanism is motivated by the Fornal–Grinstein proposal of nonstandard neutron decay channels [Fornal_2018] and by the observation that dense matter can populate dark baryons heavier than the neutron even when vacuum decay is kinematically forbidden [2018PhRvL.121f1802M]. The authors emphasize that the considered masses, $m_\chi = 1250$–$1400$ MeV, exceed $m_n$, so this is not a neutron-lifetime-anomaly scenario but rather the density-driven production of a heavier dark baryon.

Formalism

The matter composition includes nucleons, $\Lambda$, $\beta$0, $\beta$1 hyperons, the four $\beta$2 states, leptons, and $\beta$3. Meson–hyperon couplings follow SU(6) relations with optical potentials $\beta$4 MeV, $\beta$5 MeV, $\beta$6 MeV; the $\beta$7 coupling ratios are benchmarked at $\beta$8, $\beta$9, $\Delta(1232)$0. A scalar Higgs portal couples $\Delta(1232)$1 to the hadronic sector, but its mean-field contribution is shown quantitatively to be negligible: for the benchmark Yukawa coupling $\Delta(1232)$2 (saturated by the ATLAS invisible-Higgs branching limit $\Delta(1232)$3), the induced correction to $\Delta(1232)$4 is of order $\Delta(1232)$5 MeV, i.e., a fractional shift $\Delta(1232)$6. Consequently, all macroscopic effects reported arise purely from the equilibrium population of $\Delta(1232)$7, not from portal-mediated interactions — a point the authors state explicitly and repeatedly.

The conversion operator $\Delta(1232)$8 establishes chemical equilibrium between the sectors; the results apply in the weak-mixing limit where the equilibration time satisfies $\Delta(1232)$9 while mixing-induced quasiparticle shifts remain negligible. The paper concedes that determining the allowed window for $\Delta$0 requires an explicit in-medium conversion-rate calculation, which is left open.

Threshold competition between dark and conventional degrees of freedom

A central result is that the prior appearance of hyperons and $\Delta$1 resonances delays and suppresses the dark component. In pure nucleonic matter, the onset of a $\Delta$2 MeV dark baryon occurs near $\Delta$3; with hyperons and $\Delta$4s present, the redistribution of baryon number among several Fermi seas flattens the growth of $\Delta$5 and pushes the threshold to approximately $\Delta$6–$\Delta$7. For $\Delta$8 MeV, the onset in the full $\Delta$9 composition occurs at $\mu_n = \mu_\chi$0, corresponding to a stellar mass of about $\mu_n = \mu_\chi$1. The ordering of thresholds — $\mu_n = \mu_\chi$2 first (at $\mu_n = \mu_\chi$3), then $\mu_n = \mu_\chi$4 and $\mu_n = \mu_\chi$5, then $\mu_n = \mu_\chi$6 — demonstrates that $\mu_n = \mu_\chi$7 formation cannot be modeled independently of conventional non-nucleonic species.

Equation of state and stellar structure

The EOS softens once $\mu_n = \mu_\chi$8 appears, because conserved baryon number is transferred from the strongly interacting neutron sector to the weakly interacting dark component. The softening strengthens as $\mu_n = \mu_\chi$9 decreases. The maximum masses quantify this:

Composition	$\mu_n \geq m_\chi^*$0 (MeV)	$\mu_n \geq m_\chi^*$1 ($\mu_n \geq m_\chi^*$2)	$\mu_n \geq m_\chi^*$3 (km)	$\mu_n \geq m_\chi^*$4	$\mu_n \geq m_\chi^*$5 (km)
$\mu_n \geq m_\chi^*$6 only	–	2.4831	12.0432	–	13.1179
$\mu_n \geq m_\chi^*$7	1250	2.0011	13.1293	0.3420	13.1179
$\mu_n \geq m_\chi^*$8	1300	2.1136	13.0941	0.3188	13.1179
$\mu_n \geq m_\chi^*$9	1400	2.2721	12.9576	0.2951	13.1179
$m_\chi = 1250$0	1250	1.8061	12.1784	0.3105	12.3777
$m_\chi = 1250$1	1300	1.8993	12.1064	0.3105	12.3777
$m_\chi = 1250$2	1400	2.0236	11.9079	0.2362	12.3777

Relative to the purely nucleonic model, the complete compositions reduce $m_\chi = 1250$3 by roughly $m_\chi = 1250$4, $m_\chi = 1250$5, and $m_\chi = 1250$6 for the three benchmark masses. The strong implication is that the $m_\chi = 1250$7 and $m_\chi = 1250$8 MeV benchmarks fail the conventional $m_\chi = 1250$9 pulsar constraint, while $1400$0 MeV only marginally satisfies it; a linear interpolation places the crossing near $1400$1 GeV for $1400$2. The authors are careful to label this an indicative scale conditional on the assumed chemical-equilibrium limit and adopted interaction scheme, not a formal lower bound.

Canonical-mass observables are essentially insensitive to the dark sector: $1400$3 is unchanged across all three $1400$4 values in the $1400$5 sequences, indicating that canonical stars never reach the conversion threshold. Hyperons and $1400$6s reduce $1400$7 by about $1400$8 km ($1400$9).

Tidal response, sound speed, and radial composition

For GW170817-like binaries with chirp mass $m_n$0, the tidal-deformability trajectories are nearly indistinguishable across the three $m_n$1 values, confirming that the densities probed by such components lie below or marginally at the dark threshold. The response is instead governed by $m_n$2, consistent with earlier $m_n$3-admixed studies [Thapa_2021_Bary].

The squared sound speed $m_n$4 and adiabatic index $m_n$5 exhibit pronounced reductions at each particle threshold, with the $m_n$6-induced dip shifting systematically to higher density as $m_n$7 increases. All stable configurations satisfy $m_n$8.

Radial profiles for $m_n$9 MeV show that neither $\Lambda$0 nor $\Lambda$1 configurations contain visible $\Lambda$2; only the maximum-mass star develops a compact dark core confined to the inner few kilometres, with the hierarchy $\Lambda$3. This spatial localization explains why massive-pulsar constraints dominate over canonical-star constraints in this scenario.

Parameter scan

A two-dimensional scan over $\Lambda$4 MeV and $\Lambda$5 shows nearly vertical contours in $\Lambda$6, demonstrating that the maximum mass is controlled primarily by $\Lambda$7: it rises from roughly $\Lambda$8 at the light end to about $\Lambda$9 at the heavy end. The region supporting a $\beta$00 star is restricted to a narrow band near $\beta$01–$\beta$02 GeV. Canonical tidal deformabilities span $\beta$03, with the strongest variation concentrated at low $\beta$04 where $\beta$05 populates canonical stars directly.

Limitations and open questions

Several assumptions bound the interpretation of these results. First, the treatment assumes complete $\beta$06 chemical equilibrium over the stellar lifetime; no microscopic conversion-rate calculation is performed, so the predictions are conditional on the attainment of equilibrium rather than direct constraints on $\beta$07. Second, the vacuum stability of $\beta$08 above the neutron mass requires an additional protecting symmetry or suppressed interactions, which is model dependent. Third, the Higgs form factors for hyperons and $\beta$09s are set equal to the nucleonic value $\beta$10 as a simplifying input, though the resulting corrections are negligible anyway. Fourth, the preference for heavy $\beta$11 depends on the DDME2 functional, the chosen hyperon optical potentials, and the free $\beta$12-meson couplings; a finer mass scan incorporating these uncertainties has not been carried out. Open directions identified include repulsive dark-sector self-interactions, finite-temperature extensions, and cooling simulations in which out-of-equilibrium $\beta$13 reactions could modify neutrino emissivities and thermal evolution.

Conclusion

This work establishes that density-induced neutron-to-dark-baryon conversion must be treated simultaneously with hyperonic and $\beta$14 degrees of freedom: the latter delay the dark threshold, suppress the dark abundance, and thereby partially protect the EOS from maximal softening. Within the adopted scheme, astrophysical viability favors a comparatively heavy dark baryon near $\beta$15–$\beta$16 GeV, while canonical-star observables remain blind to the dark sector regardless. The dominant physical effect is the equilibrium rearrangement of composition, not Higgs-mediated interaction — a conclusion that cleanly separates this class of models from fixed-admixture dark-matter-admixed NS calculations.