Investigation of $Ξ^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory

Abstract

In the strangeness S = −2 sector, we study the Ξ − nn (I = 3/2, J P = 1/2 + ) three-body system using pionless halo effective field theory (EFT), which provides a systematic model independent framework for assessing the feasibility of light particle-stable three-body bound states, utilizing lowenergy universality. Here we take recourse to a simplistic speculation of the three-body system by eliminating the repulsive spin-singlet Ξ − n sub-system, while retaining the predominantly attractive (possibly bound) spin-triplet Ξ − n and the virtual bound spin-singlet nn sub-system. In particular, a qualitative leading order EFT investigation by introducing a sharp momentum (ultraviolet) cut-off parameter Λ c into the Faddeev-like coupled integral equations, indicates a discrete scaling behavior akin to a renormalization group limit cycle, thereby suggesting the formal existence of Efimov states in the unitary limit, as Λ c → ∞. Our subsequent non-asymptotic analysis indicates that the three-body binding energy B 3 is sensitively dependent on the cut-off without the inclusion of three-body contact interactions. Furthermore, our analysis reproduces several values of the binding energy B 3 ∼ 3−4 MeV, predicted in context of existing potential models, with the regulator Λ c in the range, ∼ 350 − 460 MeV. Finally, based on these model inputs for B 3 , a ballpark estimate of the three-body scattering length in the range, 2.6 − 4.9 fm, is naively constrained by our EFT analysis, ostensibly demonstrating the universal nature of three-body correlations that is likely to manifest themselves in a halo-bound Ξ − nn system.

Medium effects in antikaon-induced $Ξ^-$ hyperon production on nuclei near threshold

“…In view of these observations, it is interesting to note that (I) the possibility of the existence of such exotic Ξ hypernuclei as the lightest three-body ΞN N and four-body ΞN N N bound systems has been investigated in Refs. [45] and [46] using, respectively, a Gaussian Expansion Method with two modern ΞN interactions and a pionless halo effective field theory and that (II) the ground state energies of some another exotic Ξ − hypernuclei -double Ξ − hypernuclei have been calculated in Ref. [47] within the respective three-body model.…”