Light $\mathrm{\Xi }$ hypernuclei

Arguments in favor of a light $\mathrm{\Xi }NN$ hypernucleus with $\left(I\right)J^P=(3/2)1/2^{+}$ are presented, within the uncertainties of our knowledge of the baryon-baryon strangeness $-2$ interactions. If bound, this $\mathrm{\Xi }NN$ state, being decoupled from the lowest $N\mathrm{\Lambda }\mathrm{\Lambda }$ system, would be stable. It will also benefit from additional binding due to the electromagnetic interaction what makes it worthwhile to look for. We show how the equivalent state with $J=3/2$ could never be bound in spite of the attractive interaction of the two-body subsystems. We illustrate our discussion with a full-fledged Faddeev calculation of the $\mathrm{\Xi }NN$ system using simple potentials that mimic more elaborate interactions. We also make contact with different recent phenomenological interactions from the literature, like the ESC08 Nijmegen potential or quark-model based potentials.