Exploring Hyperon Skyrme Forces in Multi-$Λ$ Hypernuclei and Neutron Star Matter

A major source of uncertainty in modeling the strangeness-rich interiors of neutron stars arises from the poorly constrained two-body and three-body interactions among hyperons and nucleons. We perform a comprehensive Bayesian analysis of the $ΛΛ$ and $ΛΛN$ interaction parameters within the Skyrme Hartree-Fock framework, constrained by both hypernuclei experimental data and astrophysical observations. Our results show that the parameter space of the $ΛΛ$ interaction is tightly constrained by combining nuclear and astrophysical data, while the parameters of the $ΛΛN$ three-body interaction remain sensitive to astrophysical inputs alone. Specifically, the local, momentum-independent two-body interaction parameter $λ_0$ is tightly constrained and predominantly attractive, while the momentum-dependent parameters $λ_1$ and $λ_2$ contribute repulsive effects at high densities. A key role is played by the $ΛΛ$ potential depth in pure $Λ$ matter, which effectively constrains the two-body $ΛΛ$ interaction and governs the balance between attraction at low densities and repulsion at high densities. The repulsive components of $ΛΛ$ interactions then decrease hyperon fractions and reconcile hyperon-rich equations of state with the observed $\sim2,M_{\odot}$ neutron stars, increasing the maximum mass by up to 22%. The inclusion of $ΛΛN$ three-body forces further stiffens the EOS, raising the maximum mass by up to $\sim 0.1,M_{\odot}$. Our study represents a promising step toward a complete, experimentally grounded description of dense matter across a wide range of densities and strangeness compositions.

💡 Research Summary

The authors present a comprehensive study of hyperon–hyperon (ΛΛ) and hyperon–hyperon–nucleon (ΛΛN) interactions within the Skyrme Hartree‑Fock (SHF) framework, aiming to reduce the large uncertainties that plague the equation of state (EOS) of dense, strangeness‑rich matter in neutron stars. They adopt three widely used nucleon‑nucleon Skyrme parametrizations (SLy4, SKI3, SGI), three Λ‑nucleon parametrizations (HPΛ2, SLL4, YMR), and five ΛΛ parametrizations (SLL1, SLL2, SLL3, SLL1′, SLL3′). The ΛΛ force is written in the standard Skyrme form with a local, momentum‑independent term λ₀, momentum‑dependent terms λ₁ and λ₂, and a density‑dependent term λ₃ α that mimics three‑body effects.

A Bayesian inference scheme is constructed that simultaneously incorporates (i) experimental data from double‑Λ hypernuclei (binding energies, extracted ΛΛ potential depths) and (ii) astrophysical constraints from NICER mass–radius measurements, the tidal‑deformability constraint Λ̃ from GW170817, and the existence of ~2 M⊙ neutron stars. Prior distributions are taken broadly from the literature; the posterior is sampled using Markov Chain Monte Carlo.

Key findings are:

1. The local λ₀ parameter is tightly constrained to a negative value (≈ −300 MeV fm³), corresponding to an attractive ΛΛ potential depth U_ΛΛ≈−1 MeV in pure Λ matter. This constraint is driven mainly by the hypernuclear data.
2. The momentum‑dependent parameters λ₁ and λ₂ acquire positive values, providing a density‑dependent repulsion that becomes dominant above ≈2 ρ₀. This repulsion reduces the Λ fraction in β‑equilibrated matter, stiffens the EOS, and raises the maximum neutron‑star mass by up to 22 % (≈0.4 M⊙).
3. The density‑dependent term λ₃ α, which effectively represents a three‑body ΛΛN force, remains loosely constrained by the current astrophysical data. Including a modest repulsive λ₃ α term further increases the maximum mass by ≈0.1 M⊙.
4. The combined EOS reproduces the observed mass–radius curve (R≈12 km for a 1.4 M⊙ star) and satisfies the GW170817 tidal‑deformability band (Λ̃≈350–450).

The analysis also reveals parameter correlations: λ₀ and (λ₁, λ₂) exhibit a degeneracy where a more attractive λ₀ can be compensated by stronger repulsive λ₁, λ₂, but the hypernuclear constraints break this degeneracy, leaving a narrow allowed region. In contrast, λ₃ α and the explicit ΛΛN three‑body coupling are only weakly limited, indicating that future experiments probing ΛΛN three‑body forces (e.g., at J‑PARC, FAIR) are essential.

In conclusion, the study demonstrates that a joint nuclear‑astrophysical Bayesian analysis can tightly constrain the two‑body ΛΛ interaction, that repulsive momentum‑dependent components are crucial for reconciling hyperon‑rich matter with massive neutron stars, and that three‑body ΛΛN forces provide an additional, albeit currently uncertain, stiffening effect. The authors suggest that forthcoming double‑Λ hypernuclear measurements and direct ΛΛN three‑body experiments will further refine the hyperonic EOS and improve our understanding of dense matter.