\begin{document}$ \Lambda\Lambda N - \Xi NN $\end{document} three-body system based on two-body separable interactions to study the \begin{document}$ (I,J^P) = (1/2,1/2^+) $\end{document} three-body channel. For the \begin{document}$ \Lambda\Lambda $\end{document}, \begin{document}$ \Xi N $\end{document}, and \begin{document}$ \Lambda\Lambda - \Xi N $\end{document} amplitudes, we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration. They are characterized by the existence of a resonance just below or above the \begin{document}$ \Xi N $\end{document} threshold in the H-dibaryon channel, \begin{document}$ (i,j^p) = (0,0^+) $\end{document}. A three-body resonance appears 2.3 MeV above the \begin{document}$ \Xi d $\end{document} threshold. We show that if the \begin{document}$ \Lambda\Lambda - \Xi N $\end{document} H-dibaryon channel is not considered, the \begin{document}$ \Lambda\Lambda N - \Xi NN $\end{document} S wave resonance disappears. Thus, the possible existence of a \begin{document}$ \Lambda\Lambda N - \Xi NN $\end{document} resonance would be sensitive to the \begin{document}$ \Lambda\Lambda - \Xi N $\end{document} interaction. The existence or nonexistence of this resonance could be evidenced by measuring, for example, the \begin{document}$ \Xi d $\end{document} cross section."> <inline-formula><tex-math id="M1-4">\begin{document}$ {{ \Lambda}{ \Lambda}{ N} { -} { \Xi} { N}{ N}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/874b8c14-0ce4-4019-8efb-df027b7b7eb6/CPC-2020-0303_M1-4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/874b8c14-0ce4-4019-8efb-df027b7b7eb6/CPC-2020-0303_M1-4.png"/></alternatives></inline-formula> <i>S</i> wave resonance -
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