Light $\Xi$ hypernuclei

Abstract

Arguments in favor of a light $\Xi NN$ hypernucleus with $(I)J^P=(3/2)1/2^{+}$ are presented, within the uncertainties of our knowledge of the baryon-baryon strangeness $-2$ interactions. If bound, this $\Xi NN$ state, being decoupled from the lowest $N\Lambda \Lambda$ 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 $\Xi NN$ 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.

7 pages. To be published in Phys. Rev. C. Refs. [10] and [15] have been corrected

References in corpus (4)

• $\Lambda NN$ and $\Sigma NN$ systems at threshold
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• $\Lambda NN$ and $\Sigma NN$ systems at threshold: II. The effect of D waves
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• Investigation of ${\Xi }^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory