${}_{ΛΛ}^{5}$H and ${}_{ΛΛ}^{5}$He Hypernuclei reexamined in Halo/Cluster Effective Theory

Abstract

The J = 1/2 iso-doublet double-Λ hypernuclei, namely, 5 ΛΛ H and 5 ΛΛ He, are examined as the three-body cluster states, ΛΛt (t ≡ 3 H or triton) and ΛΛh (h ≡ 3 He or helion), respectively, in a model independent framework utilizing pionless halo effective field theory. Both singlet and triplet states of the ΛT (T ≡ t, h) subsystems are used in the elastic channel for the study of 4 Λ H−Λ and 4 Λ He−Λ scattering processes. A prototypical leading order investigation yields a ΛΛ separation energy (BΛΛ) of 5 ΛΛ He greater than that of 5 ΛΛ H, in agreement with the existing results from rigorous Faddeev calculation analyses using potential model framework. In particular, our study of the sharp momentum cut-off dependence of the non-asymptotic solutions to the coupled integral equations, upon normalization with respect to a single potential model predicted (BΛΛ , aΛΛ) data point (aΛΛ being the S-wave ΛΛ scattering length) for each ΛΛT iso-doublet, yields results with reasonably good agreement with potential model analyses for cut-off scales close to Λc ∼ 230 − 240 MeV. This is consistent with low-energy ΛΛ interaction mechanism dominated by two π or σ meson exchange. Finally, we present a preliminary estimate of the S-wave ΛΛT three-body scattering lengths at the leading order in the effective theory for several input values of aΛΛ which were earlier predicted from several existing phenomenological analyses.

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

“…Such modified π / EFT analyses have been successfully extended to study light hypernuclei, since the very first in 2002 by Hammer [67] on the LO investigation of hypertriton ( 3 Λ H) as a (I = 0, J = 1/2) ΛNN Efimov-like bound system. Subsequently, a number of halo/cluster EFT works based on similar LO analysis appeared in the literature, both in the S = −1 [68,69] and S = −2 [70][71][72] strangeness sectors, in the search for exotic single and double-Λ hypernuclear states, e.g., nnΛ, 1 4 ΛΛ He, 5 ΛΛ H, 5 ΛΛ He and 6 ΛΛ He. It is worth mentioning here that a novel ab initio LO π / EFT technique using few-body stochastic variational method of calculation was initially suggested in Refs.…”

“…the corresponding reduced mass of three-body (particle-dimer) system. The construction methodology of these integrals equation is similar to those employed in several earlier π / EFT works [68,[70][71][72]88]. The renormalized S-wave projected coupled channel elastic and inelastic integral equations with the introduced UV sharp momentum cut-off Λ c are respectively given as 2 The value B 2 which corresponds to the the pole position of the u 1 dibaryon propagator in our halo EFT formalism may be compared to the binding energy of the putative (1,1) ΞN bound state (D * ) predicted in the potential model analyses in Refs.…”