Repulsive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Λ</mml:mi></mml:math> potentials in dense neutron star matter and binding energy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Λ</mml:mi></mml:math> in hypernuclei

Abstract

The repulsive three-body force between the lambda ($\mathrm{\ensuremath{\Lambda}}$) hyperon and medium nucleons is a key element in solving the hyperon puzzle in neutron stars. We investigate the binding energies of the $\mathrm{\ensuremath{\Lambda}}$ hyperon in hypernuclei to verify the repulsive $\mathrm{\ensuremath{\Lambda}}$ potentials from the chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) employing the Skyrme Hartree-Fock method. We find that the $\ensuremath{\chi}\mathrm{EFT}\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Lambda}}$ potential with $\mathrm{\ensuremath{\Lambda}}NN$ three-body forces reproduces the existing hypernuclear binding energy data, whereas the $\mathrm{\ensuremath{\Lambda}}$ binding energies are overestimated without the $\mathrm{\ensuremath{\Lambda}}NN$ three-body force. Additionally, we search for the parameter space of the $\mathrm{\ensuremath{\Lambda}}$ potentials by varying the Taylor coefficients of the $\mathrm{\ensuremath{\Lambda}}$ potential and the effective mass of $\mathrm{\ensuremath{\Lambda}}$ at the saturation density. Our analysis demonstrates that the parameter region consistent with the $\mathrm{\ensuremath{\Lambda}}$ binding energy data spans a wide range of the parameter space, including even more repulsive potentials than the $\ensuremath{\chi}\mathrm{EFT}$ prediction. We confirm that these strong repulsive $\mathrm{\ensuremath{\Lambda}}$ potentials suppress the presence of $\mathrm{\ensuremath{\Lambda}}$ in neutron star matter. We found that the $\mathrm{\ensuremath{\Lambda}}$ potentials repulsive at high densities are favored when the depth of the $\mathrm{\ensuremath{\Lambda}}$ potential at the saturation density, ${U}_{\mathrm{\ensuremath{\Lambda}}}({\ensuremath{\rho}}_{0})={J}_{\mathrm{\ensuremath{\Lambda}}}$, is ${J}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\gtrsim}\ensuremath{-}29\phantom{\rule{4pt}{0ex}}\text{MeV}$, while attractive ones are favored when ${J}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\lesssim}\ensuremath{-}31\phantom{\rule{4pt}{0ex}}\text{MeV}$. This suggests that future high-resolution data of hypernuclei could rule out the scenario in which $\mathrm{\ensuremath{\Lambda}}$'s appear through the precise determination of ${J}_{\mathrm{\ensuremath{\Lambda}}}$ within the accuracy of $1\phantom{\rule{4pt}{0ex}}\text{MeV}$.

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