论文标题
美元
${}_{ΛΛ}^{5}$H and ${}_{ΛΛ}^{5}$He Hypernuclei reexamined in Halo/Cluster Effective Theory
论文作者
论文摘要
j = 1/2 iso-doublet double- $ c $ hypernuclei，即$ {} _ {} _ {λλ}^{5} $ h和$ {} _ {λλ}^{5} $ he，被检查为三型群集$（$λλT$（$ te） $λλH$（$ h \ equiv {}^3 $ He或Helion）在使用Pionless Halo有效理论的模型独立框架中。弹性频道中使用了组成$λt$（$ t \ equiv t，h $）子系统的单元和三重态。使用急剧动量截止调节器进行的原型领先顺序研究，无论选择的弹性频道的类型如何，都可以为三体结合能的截止依赖性或双重$λ$分离能量（$ b_ {λλλ} $）提供给镜面伴侣，明显地表明了这些三分之二的体系，可以获得镜面伴侣。随后，根据我们对每种镜像超核的潜在模型分析的一对输入数据的归一化解决方案，从而产生了$ b_ {λλ} $，该$非常同意，该模型与我们选择的各种erstWhile调节器的潜在模型相当良好，以适用于我们选择的截止型号，以选择我们选择的截止器调节器，$ \ simer $ \ sim $ \ \ \ \ \ \ \ \ mev。这要么与无疑的有效理论一致，要么与其略微增强版本的硬尺度约为$2M_π$，其中低能量$λ$ - $λ$-λ$互动由$ππ$或$σ$ -Meson Exchange主导。最后，为了证明我们有效理论的可预测性，我们提出了S波$λλT$三体散射长度和$λ$ - 分离能的初步估计。
The J=1/2 iso-doublet double-$Λ$-hypernuclei, namely, ${}_{ΛΛ}^{5}$H and ${}_{ΛΛ}^{5}$He, are examined as the three-body cluster states, $ΛΛt$ ($t\equiv {}^3$H or triton) and $ΛΛh$ ($h\equiv {}^3$He or helion), respectively, in a model independent framework utilizing pionless halo effective theory. Both singlet and triplet states of the constituent $ΛT$ ($T\equiv t,h$) sub-system are used in the elastic channel for the study of $_Λ^4$H$-Λ$ and $_Λ^4$He$-Λ$ scattering processes. A prototypical leading order investigation using a sharp momentum cut-off regulator, irrespective of the type of the elastic channel chosen, yields almost identical cut-off dependence of the three-body binding energy or the double-$Λ$-separation energy ($B_{ΛΛ}$) is obtained for the mirror partners, evidently suggesting good isospin symmetry in these three-body systems. Subsequently, upon normalization of our solutions to the integral equation with respect to a single pair of input data from an {\it ab initio} potential model analysis for each mirror hypernuclei, yields $B_{ΛΛ}$ which agrees fairly well with various erstwhile regulator independent potential models for our choice of the cut-off regulator, $\sim 200$ MeV. This is either consistent with pionless effective theory or with its slightly augmented version with a hard scale around $2m_π$, where low-energy $Λ$-$Λ$ interactions dominated by $ππ$ or $σ$-meson exchange. Finally, to demonstrate the predictability of our effective theory, we present preliminary estimates of the S-wave $ΛΛT$ three-body scattering lengths and the $Λ$-separation energies.
