Nature of the $\Lambda nn$ $(J^\pi=1/2^+, I=1)$ and ${\rm ^3_\Lambda H^*} (J^\pi=3/2^+, I=0)$ states

The nature of the $\Lambda nn$ and ${\rm ^3_\Lambda H^*} (J^\pi=3/2^+,~I=0)$ states is investigated within a pionless effective field theory at leading order, constrained by the low energy $\Lambda N$ scattering data and hypernuclear 3- and 4-body data. Bound state solutions are obtained using the stochastic variational method, 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 $\Lambda nn$ and ${\rm ^3_\Lambda H^*}$ states unbound. We conclude that the excited state ${\rm ^3_\Lambda H^*}$ is a virtual state and the $\Lambda nn$ pole located close to the three-body threshold in a complex energy plane could convert to a true resonance with Re$(E)>0$ for some considered $\Lambda N$ interactions. Finally, the stability of resonance solutions is discussed and limits of the accuracy of performed calculations are assessed.