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

Abstract

The nature of the $\Lambda nn$ and ${}_{\mathrm{\Lambda }}^3{\mathrm{H}}^{\ast }(J^{\pi }=3/2^{+},I=0)$ 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 ${}_{\mathrm{\Lambda }}^3{\mathrm{H}}^{\ast }$ states unbound. We conclude that the excited state ${}_{\mathrm{\Lambda }}^3{\mathrm{H}}^{\ast }$ 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.

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• Few nucleons scattering in pionless effective field theory
• The cross-section measurement for the ${}^3\text{H}(e,e^{\prime }{K}^{+})nn\Lambda$ reaction
• Systematic Nuclear Uncertainties in the Hypertriton System
• Consequences of increased hypertriton binding for $s$-shell $\Lambda$-hypernuclear systems
• Spectrum of light nuclei in a finite volume
• Study on $\Lambda nn$ Bound State and Resonance
• Machine learning the single-$\Lambda$ hypernuclei with neural-network quantum states