Impact of $Ξ$-Hypernuclear Constraints on Relativistic Equation of States and Properties of Hyperon Stars

Abstract: Significant uncertainties persist in describing the equation of state and internal structure of hyperon stars due to the limited understanding of the mechanisms underlying hyperon interactions. Constraining the interaction parameter space through a combination of the latest astronomical observations and hypernuclear physics experiments is therefore essential. In this study, we incorporate experimental constraints from $\Xi$ hypernuclear physics on top of $\Lambda$ hyperons considered in \citet{Sun2023APJ942.55}. Specifically, based on updated measurements of hyperon separation energies from $\Xi$ hypernuclear experiments, sets of $\Xi N$ effective interactions are constructed and a linear correlation between their scalar ($\sigma$) and vector ($\omega$) coupling strength ratios is proposed as a constraint derived from $\Xi$ hypernuclear physics. Together with experimental correlations and astronomical observational data, four types of analyses are performed to constrain hyperon-nucleon interactions and the properties of hyperon stars. Compared to the vector $\omega$ meson-hyperon coupling, the introduction of linear correlations in hypernuclear physics imposes a more substantial constraint on the scalar $\sigma$ meson-hyperon coupling, significantly enhancing its coupling strength and thereby ensuring the stiffness of the equation of state, highlighting the crucial role of hypernuclear studies in solving the hyperon puzzle problem. Consequently, a maximum mass of around $2M_{\odot}$ can be achieved with all five interactions considered in this study under the combined constraints from astronomical observations and nuclear physics. With more reliably estimated hyperon-nucleon contributions, the uncertainties in both the fractions and the threshold densities at which hyperons appear inside neutron stars are notably reduced, along with those in the mass-radius predictions.