Repulsive $\Lambda$ potentials in dense neutron star matter and binding energy of $\Lambda$ in hypernuclei

TL;DR

This study investigates the repulsive three-body forces involving the lambda hyperon in dense neutron star matter, using hypernuclear data to constrain the potentials and implications for hyperon presence in neutron stars.

Contribution

It demonstrates that the $ ext{chi}$EFT $ ext{Lambda}$ potential with three-body forces reproduces hypernuclear binding energies and constrains the density-dependent $ ext{Lambda}$ potentials relevant for neutron star matter.

Findings

$ ext{chi}$EFT $ ext{Lambda}$ potential with three-body forces matches hypernuclear data.

Strongly repulsive $ ext{Lambda}$ potentials suppress hyperon appearance in neutron stars.

Future hypernuclear measurements can constrain $ ext{Lambda}$ potential depth, affecting neutron star models.

Abstract

The repulsive three-body force between the lambda ($\Lambda$) hyperon and medium nucleons is a key element in solving the hyperon puzzle in neutron stars. We investigate the binding energies of $\Lambda$ hyperon in hypernuclei to verify the repulsive $\Lambda$ potentials from the chiral effective field theory ($\chi$EFT) employing the Skyrme Hartree-Fock method. We find that the $\chi$EFT $\Lambda$ potential with the $\Lambda NN$ three-body forces reproduces the existing hypernuclear binding energy data, whereas the $\Lambda$ binding energies are overestimated without the $\Lambda NN$ three-body force. Additionally, we search for the parameter space of the $\Lambda$ potentials by varying the Taylor coefficients of the $\Lambda$ potential and the effective mass of $\Lambda$ at the saturation density. Our analysis demonstrates that the parameter region consistent with the $\Lambda$ binding energy data spans a wide range of the parameter space, including even more repulsive potentials than the $\chi$EFT prediction. We confirm that these strong repulsive $\Lambda$ potentials suppress the presence of $\Lambda$ in the neutron star matter. We found that the $\Lambda$ potentials repulsive at high densities are favored when the depth of the $\Lambda$ potential at the saturation density, $U_\Lambda(\rho_0)=J_\Lambda$, is $J_\Lambda\gtrsim-29~\text{MeV}$, while attractive ones are favored when $J_\Lambda \lesssim -31~\text{MeV}$. This suggests that the future high-resolution data of hypernuclei could rule out the scenario in which $\Lambda$s appear through the precise determination of $J_\Lambda$ within the accuracy of $1~\text{MeV}$.