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

Faddeev calculations suggest that: (i) B-LambdaLambda (He-6(LambdaLambda)) for the recent KEK emulsion event is compatible with fairly weak LambdaLambda potentials V-LambdaLambda such as due to the Nijmegen soft-core NSC97 model; (ii) the isodoublet H-5(LambdaLambda) - He-5(LambdaLambda) hypernuclei are particle-stable even in the limit V-LambdaLambda --> 0; and (iii) H-4(LambdaLambda) within a LambdaLambdad model is particle-stable. However, fourbody LambdaLambdapn Faddeev-Yakubovsky calculations do not produce a bound state for H-4(LambdaLambda) even for V-LambdaLambda considerably stronger than required to reproduce B-LambdaLambda(He-6(LambdaLambda)), in contrast to the normal situation (e.g. Be-10(LambdaLambda)) where a four-body Faddeev-Yakubovsky calculation yields stronger binding than that due to a suitably defined three-body Faddeev calculation. For strangers systems, Faddeev calculations using LambdaXi interactions which simulate model NSC97 suggest that He-6(LambdaXi) marks the onset of nuclear stability for Xi hyperons.