Constraining the $\Lambda\Lambda$ interaction with terrestrial and astronomical data

Terrestrial double-$\Lambda$ hypernuclear data and astronomical observations of neutron stars provide complementary constraints on the $\Lambda\Lambda$ interaction. In this work, we investigate the $\Lambda\Lambda$ interaction within a Skyrme energy density functional framework based on the KIDS (Korea-IBS-Daegu-SKKU) models. We employ a Skyrme-type $\Lambda\Lambda$ interaction that includes the standard $s$- and $p$-wave terms, as well as a density-dependent term that effectively represents an $N\Lambda\Lambda$ three-body force. The $s$-wave terms are constrained using data on double-$\Lambda$ hypernuclei supplemented by pseudodata obtained from core + $2\Lambda$ three-body model calculations including heavier hypernuclei. We show that the data on heavier systems are essential to simultaneously constrain the two $s$-wave parameters. We further explore the impact of the $p$-wave and $N\Lambda\Lambda$ components on the neutron-star properties and find that appropriate repulsive contributions of these terms yield consistency with current neutron-star mass-radius observations. These results indicate that the present framework provides phenomenologically acceptable equations of state for dense $(N,\Lambda)$ matter over a wide range of densities and highlight the importance of future experimental data on heavier double-$\Lambda$ hypernuclei.