Nature of the $Λnn$ $(J^π=1/2^+, I=1)$ and ${\rm ^3_ΛH^*} (J^π=3/2^+, I=0)$ states

Abstract

The nature of the $Λnn$ and ${\rm ^3_ΛH^*} (J^π=3/2^+,~I=0)$ states is investigated within a pionless effective field theory at leading order, constrained by the low energy $ΛN$ 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 $Λnn$ and ${\rm ^3_ΛH^*}$ states unbound. We conclude that the excited state ${\rm ^3_ΛH^*}$ is a virtual state and the $Λnn$ 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 $ΛN$ interactions. Finally, the stability of resonance solutions is discussed and limits of the accuracy of performed calculations are assessed.