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

Abstract

We investigate the existence of bound $\Xi$ \break states in systems with $A=4-7$ baryons using the Jacobi NCSM approach in combination with chiral NN and $\Xi$N interactions. We find three shallow bound states for the NNN$\Xi$ system (with $(J^{\pi },T)=(1^{+},0)$, $(0^{+},1)$ and $(1^{+},1)$) with quite similar binding energies. The ${}_{\Xi }^5\mathrm{H}({\frac{1}{2}}^{+},\frac{1}{2})$ and ${}_{\Xi }^7\mathrm{H}({\frac{1}{2}}^{+},\frac{3}{2})$ hypernuclei are also clearly bound with respect to the thresholds ${}^4\mathrm{He}+\Xi$ and ${}^6\mathrm{He}+\Xi$, respectively. The binding of all these $\Xi$ systems is predominantly due to the attraction of the chiral $\Xi$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.

Comments: 12 pages, 2 figures