Nature of the Λ n n ( J π = 1 / 2 + , I = 1 ) and Λ 3 H * ( J π = 3 / 2 + , I = 0 ) states

The nature of the $\mathrm{\ensuremath{\Lambda}}nn$ and $_{\mathrm{\ensuremath{\Lambda}}}^{3}\mathrm{H}^{*}({J}^{\ensuremath{\pi}}=3/{2}^{+},\phantom{\rule{4pt}{0ex}}I=0)$ states is investigated within a pionless effective field theory at leading order, constrained by the low-energy $\mathrm{\ensuremath{\Lambda}}N$ scattering data and hypernuclear three- and four-body data. Bound-state solutions are obtained using the stochastic variational method, and the continuum region is studied by employing two independent methods: the inverse analytic continuation in the coupling constant method and the complex scaling method. Our calculations yield both the $\mathrm{\ensuremath{\Lambda}}nn$ and $_{\mathrm{\ensuremath{\Lambda}}}^{3}\mathrm{H}^{*}$ states unbound. We conclude that the excited state $_{\mathrm{\ensuremath{\Lambda}}}^{3}\mathrm{H}^{*}$ is a virtual state and the $\mathrm{\ensuremath{\Lambda}}nn$ pole located close to the three-body threshold in a complex energy plane could convert to a true resonance with $\mathrm{Re}(E)g0$ for some considered $\mathrm{\ensuremath{\Lambda}}N$ interactions. Finally, the stability of resonance solutions is discussed and limits of the accuracy of performed calculations are assessed.