To bind or not to bind: ΛΛ hypernuclei and Ξ hyperons

Faddeev calculations suggest that: (i) B_ΛΛ(_ΛΛ⁶He) for the recent KEK emulsion event is compatible with fairly weak ΛΛ potentials V_ΛΛ such as due to the Nijmegen soft-core NSC97 model; (ii) the isodoublet _ΛΛ⁵H - _ΛΛ⁵He hypernuclei are particle-stable even in the limit V_ΛΛ → 0; and (iii) _ΛΛ⁴H within a ΛΛd model is particle-stable. However, four-body ΛΛpn Faddeev-Yakubovsky calculations do not produce a bound state for _ΛΛ⁴H even for V_ΛΛ considerably stronger than required to reproduce B_ΛΛ(_ΛΛ⁶He), in contrast to the normal situation (e.g. _ΛΛ¹⁰Be) where a four-body Faddeev-Yakubovsky calculation yields stronger binding than that due to a suitably defined three-body Faddeev calculation. For stranger systems, Faddeev calculations using λ Ξ interactions which simulate model NSC97 suggest that _ΛΞ⁶He marks the onset of nuclear stability for Ξ hyperons.