Deeply bound $\Xi$ tribaryon

Abstract

We have used realistic local interactions based on the recent update of the strangeness $-2$ Nijmegen ESC08c potential to calculate the bound state problem of the $\Xi NN$ system in the $(I)J^P=(\frac{1}{2})\frac{3}{2}^+$ state. We found that this system presents a deeply bound state lying $13.5$ MeV below the $\Xi d$ threshold. Since in lowest order, pure S$-$wave configuration, this system can not decay into the open $\Lambda\Lambda N$ channel, its decay width is expected to be very small. We have also recalculated the $(I)J^P=(\frac{3}{2})\frac{1}{2}^+$ state and we have compared with results of quark-model based potentials.