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

• Received 24 July 2020
• Accepted 2 February 2021

DOI:https://doi.org/10.1103/PhysRevC.103.025204