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.

中文翻译：

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Λnn（Jπ= 1/2 +，I = 1）和Λ3H*（Jπ= 3/2 +，I = 0）状态的性质

的性质 $\mathrm{\Lambda }ññ$ 和 ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}^{*}（{Ĵ}^{\pi }=3/2^{+}，\mathrm{一世}=0）$ 在低能约束的无偶有效场理论下以无序的形式研究状态 $\mathrm{\Lambda }ñ$散射数据和超核三体和四体数据。使用随机变分方法获得束缚态解，并通过两种独立的方法研究连续体区域：耦合常数方法中的逆解析连续性和复标度方法。我们的计算得出$\mathrm{\Lambda }ññ$ 和 ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}^{*}$状态未绑定。我们得出结论，兴奋状态${}_{\mathrm{\Lambda }}{}^3\mathrm{H}^{*}$ 是一种虚拟状态， $\mathrm{\Lambda }ññ$ 位于复杂能量平面中靠近三体阈值的极点可以转换为真实的共振 $\mathrm{回覆}（Ë）>0$ 对于一些考虑 $\mathrm{\Lambda }ñ$互动。最后，讨论了共振解的稳定性，并评估了执行计算的精度极限。