Five-body cluster structure of double-$\Lambda$ hypernucleus $^{11}_{\Lambda \Lambda}$Be

Energy levels of the double $\Lambda$ hypernucleus, $^{11}_{\Lambda \Lambda}$Be are calculated within the framework of an $\alpha \alpha n \Lambda \Lambda$ five-body model. Interactions between constituent particles are determined so as to reproduce reasonably the observed low-energy properties of the $\alpha \alpha$, $\alpha \alpha n$ nuclei and the existing data for $\Lambda$-binding energies of the $\alpha \Lambda$, $\alpha \alpha \Lambda$, $\alpha n \Lambda$ and $\alpha \alpha n \Lambda$ systems. An effective $\Lambda \Lambda$ interaction is constructed so as to reproduce, within the $\alpha \Lambda \Lambda$ three-body model, the $B_{\Lambda \Lambda}$ of $^6_{\Lambda \Lambda}$He, which was extracted from the emulsion experiment, the NAGARA event. With no adjustable parameters for the $\alpha \alpha n \Lambda \Lambda$ system, $B_{\Lambda \Lambda}$ of the ground and bound excited states of $^{11}_{\Lambda \Lambda}$Be are calculated with the Gaussian Expansion Method. The Hida event, recently observed at KEK-E373 experiment, is interpreted as an observation of the ground state of the $^{11}_{\Lambda \Lambda}$Be.