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

TL;DR

This study constrains the $\Lambda\Lambda$ interaction using terrestrial hypernuclear data and neutron star observations within a Skyrme energy density framework, emphasizing the importance of heavy hypernuclei data for accurate modeling.

Contribution

It introduces a comprehensive Skyrme-type $\Lambda\Lambda$ interaction model constrained by hypernuclear and astrophysical data, including a density-dependent term representing three-body forces.

Findings

Heavy hypernuclear data are crucial for constraining $\Lambda\Lambda$ interaction parameters.

Appropriate repulsive $\Lambda\Lambda$ terms align neutron star models with observations.

The framework yields realistic equations of state for dense matter across various densities.

Abstract

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.