$A=4-7$ $Ξ$ hypernuclei based on interactions from chiral effective field theory

We investigate the existence of bound $Ξ$ \break states in systems with $A=4-7$ baryons using the Jacobi NCSM approach in combination with chiral NN and $Ξ$N interactions. We find three shallow bound states for the NNN$Ξ$ system (with $(J^π,T)=(1^+,0)$, $(0^+,1)$ and $(1^+,1)$) with quite similar binding energies. The $^5_Ξ\mathrm{H}(\frac{1}{2}^+,\frac{1}{2})$ and $^7_Ξ\mathrm{H}(\frac{1}{2}^+,\frac{3}{2})$ hypernuclei are also clearly bound with respect to the thresholds $^4\mathrm{He} + Ξ$ and $^6\mathrm{He} +Ξ$, respectively. The binding of all these $Ξ$ systems is predominantly due to the attraction of the chiral $Ξ$N potential in the $^{33}S_1$ channel. A perturbative estimation suggests that the decay widths of all the observed states could be rather small.

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