Evolution of strangeness and hyperons in quarkyonic matter

We study the evolution of matter composition from nuclear to quark densities in the confining regime, by extending an ideal model of Quarkyonic matter, IdylliQ model, to multi-flavor systems including strangeness. The model provides a dual description of quark and baryon occupation probabilities which are determined by minimizing the energy of the system. Saturation of low-momentum quark states drives the formation of quark matter and constrains baryon distributions, inducing statistical repulsion among baryon species. Applying the model to charge-neutral matter composed of neutrons, $Λ_0$, and $Σ_0$ hyperons, we find that, for typical size of baryons, $d$-quark saturation occurs before hyperons appear, delaying their onset and shifting the threshold density from $\sim 2$–$3n_{\rm sat}$ to $\sim 5$–$6n_{\rm sat}$ ($n_{\rm sat} \approx 0.16,{\rm fm^{-3}}$: nuclear saturation density). After hyperons emerge, low-momentum hyperon states remain only sparsely occupied due to the quark saturation. These features mitigate the hyperon puzzle, in which the appearance of hyperons softens neutron star equations of state significantly by increasing energy density with little pressure increase. Our results highlight the key role of quark saturation in dense baryonic matter and provide new insights into the interplay between quark dynamics and hyperon physics in neutron stars.

💡 Research Summary

The paper extends the previously proposed ideal dual Quarkyonic (IdylliQ) model to a three‑flavor system that includes strangeness, thereby allowing a quantitative study of how matter composition evolves from nuclear to quark densities in the confining regime. The original IdylliQ framework provides a dual description of quark and baryon occupation probabilities through the relation
(f_q(\mathbf q)=\int d^3k,\phi(\mathbf q-\mathbf k/N_c),f_B(\mathbf k)),
where (\phi) encodes the momentum spread of a confined quark inside a baryon of size (\sim\Lambda_{\rm QCD}^{-1}). By minimizing the total energy density under the constraint of fixed baryon number, the authors obtain a self‑consistent solution in which low‑momentum quark states become saturated first (the “quark saturation” point). This saturation occurs at a baryon density of order (n_B\simeq2,n_{\rm sat}) for typical baryon size parameters, far below the QCD scale.

In the multi‑flavor extension the authors consider charge‑neutral matter composed of neutrons (udd), the isosinglet hyperon (\Lambda^0) (uds) and the isotriplet (\Sigma^0) (uds). Because the d‑quark sector saturates before hyperons appear, the Pauli‑blocking effect of the filled d‑quark sea imposes a statistical repulsion among different baryon species. Consequently, the chemical potential at which a neutron can decay into a hyperon is shifted from the naïve condition (\mu_n=M_Y) to a higher threshold
(\mu_n = 2M_Y - M_N).
This extra term, (M_Y-M_N), represents the energy cost of opening low‑momentum d‑quark phase space for the hyperon. Numerically, the hyperon onset is pushed from the conventional (2!-!3,n_{\rm sat}) range to roughly (5!-!6,n_{\rm sat}).

After hyperons appear, the model predicts that their low‑momentum states are only sparsely occupied, with an occupation probability scaling as (\sim 1/N_c^3). Thus hyperons are forced to populate higher momentum shells, which limits their contribution to the pressure while still increasing the energy density. This mechanism softens the equation of state (EoS) far less dramatically than in traditional hyperonic models, thereby mitigating the long‑standing “hyperon puzzle” (the conflict between hyperon‑induced softening and observed massive neutron stars).

The authors also examine the doubly‑strange hyperon (\Xi^0) (uss), which is not subject to d‑quark saturation because it contains only s‑quarks. In this case low‑momentum states can be fully occupied, leading to a much stronger softening of the EoS. However, the onset density for (\Xi^0) is also found to be around (5!-!6,n_{\rm sat}), likely beyond the central densities of typical neutron stars, so its impact on observable stellar properties may be limited.

Overall, the paper demonstrates that quark‑saturation effects provide a natural statistical repulsion among baryons, delay hyperon appearance, and reduce the severity of EoS softening. The work suggests that incorporating quark Pauli blocking into hybrid quark‑baryon models is essential for a realistic description of dense matter. Future extensions should include realistic nucleon‑hyperon and hyperon‑hyperon interactions, possible modifications of the baryon internal structure at high density, and confrontation with astrophysical constraints from neutron‑star mass–radius measurements and gravitational‑wave observations.