Exploring Hyperon Skyrme Forces in Multi-$\Lambda$ 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 $\Lambda\Lambda$ 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 $\sim2\,M_{\odot}$ neutron stars, increasing the maximum mass by up to 22\%. The inclusion of $\Lambda\Lambda N$ 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.