Evolution of strangeness and hyperons in quarkyonic matter

Abstract

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.

Figures (6)

• Figure 1: Comparison of the previous model of Quarkyonic matter and IdylliQ model. In the previous modeling, there is a discrepancy between the Fermi momenta of $u$ and $d$ quarks, so the $u$-quark distribution has a mismatch with the nucleon distribution. Meanwhile, in the IdylliQ picture, this mismatch is naturally resolved by considering the half-occupied distribution for the $u$ quark that is dual to the nucleonic description.
• Figure 2: Phase-space density distribution for baryons (left) and quarks (right). We use $M_N = 0.94\,\text{GeV}$ and $M_Y = 1.12\,\text{GeV}$ ($\approx M_\Lambda < M_{\Sigma_0} \approx 1.19\,\text{GeV}$). In the left panel, $k_{\mathrm{F}n, \mathrm{ideal}}$ and $k_{\mathrm{F}Y, \mathrm{ideal}}$ refer to the Fermi momentum of $n$ and $Y$ in the ideal Fermi gas picture without quark saturation effect taken into account, respectively.
• Figure 3: Comparison of the equations of state between the pure neutron matter and the hyperon matter at $\Lambda = 0.4$ GeV. Left: Pressure as a function of $n_B$. Right: Speed of sound as a function of $n_B$.
• Figure 4: Phase-space density distribution for baryons (left) and quarks (right). In the left panel, $k_{\mathrm{F}n, \mathrm{ideal}}$ and $k_{\mathrm{F}Y, \mathrm{ideal}}$ refer to the Fermi momentum of $n$ and $Y$ in the ideal Fermi gas picture without quark saturation effect taken into account, respectively. Note that in the ideal Fermi gas picture, the $\Xi^0$ threshold has not reached yet.
• Figure 5: Comparison of the energy density at a given baryon density among the pure neutron matter, the $S=-1$ hyperon matter, and the hyperon matter with $\Xi^0$.