Constraining the repulsion of the Λ potential at high densities through Λ binding energy of hypernuclei

The hyperon puzzle in neutron stars, extensively discussed in recent decades, refers to the problem that most of the equations of state with hyperons are not sufficiently stiff to support the observed massive neutron stars. Although various solutions to the puzzle have been proposed, the presence or absence of hyperons in neutron stars remains uncertain. The Λ potential at high densities is a key ingredient in discussing the presence of Λ hyperons, but it is not well constrained by the available experimental data.

High-resolution data of the Λ binding energy in hypernuclei will become available in future experiments at J-PARC. In this presentation, we explore the possibility of constraining the repulsion of Λ potential at high densities using the Λ binding energy data. We parametrize the Λ potential by the Taylor coefficients and the effective mass at the saturation density. We then vary the parameters, calculate the Λ binding energy using the Skyrme-Hartree-Fock method, and compare the results with the available data. We found that the repulsive (attractive) Λ potentials at high densities are favored when the depth of the Λ potential at saturation density, J_Λ, is J_Λ ≥ -29 MeV (J_Λ ≤ -31 MeV). Since the value of J_Λ is sensitive to the Λ binding energy, this result suggests that future high-resolution data could exclude the scenario in which Λ hyperons appear in neutron stars.