Study on $\Lambda nn$ Bound State and Resonance

We perform the ab initio no-core shell model (NCSM) calculation to investigate the bound state problem of the three-body $\Lambda nn$ system in chiral next-to-next-to-leading-order NN and chiral leading-order YN interactions. The calculations show that no $\Lambda nn$ bound state exists, but predict a low-lying $\Lambda nn$ resonant state near the threshold with the energy of $E_r= 0.124$ MeV and the width of about $\Gamma=1.161$ MeV. In searching for $\Lambda nn$ resonances, we extend the NCSM calculation to the continuum state by employing the J-matrix formalism in the scattering theory with the hyperspherical oscillator basis.