Exploring hyperon Skyrme forces in multi-Λ hypernuclei and neutron star matter

ABSTRACT A major source of uncertainty in modelling 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 $\Lambda \Lambda$ and $\Lambda \Lambda N$ 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 $\Lambda \Lambda$ interaction is tightly constrained by combining nuclear and astrophysical data, while the parameters of the $\Lambda \Lambda N$ three-body interaction remain sensitive to astrophysical inputs alone. Specifically, the local, momentum-independent two-body interaction parameter $\lambda _0$ is tightly constrained and predominantly attractive, while the momentum-dependent parameters $\lambda _1$ and $\lambda _2$ contribute repulsive effects at high densities. A key role is played by the $\Lambda \Lambda$ potential depth in pure $\Lambda$ matter, which effectively constrains the two-body $\Lambda \Lambda$ interaction and governs the balance between attraction at low densities and repulsion at high densities. The repulsive components of $\Lambda \Lambda$ interactions then decrease hyperon fractions and reconcile hyperon-rich equations of state with the observed $\sim 2\, {\rm M}_{\odot }$ neutron stars, increasing the maximum mass by up to 22 percent. The inclusion of $\Lambda \Lambda N$ three-body forces further stiffens the equation of state, raising the maximum mass by up to $\sim 0.1\, {\rm M}_{\odot }$. Our study represents a promising step towards a complete, experimentally grounded description of dense matter across a wide range of densities and strangeness compositions.