论文标题
$蒜
Investigation of $Ξ^{-}nn$ ($S=-2$) Hypernucleus in Low-energy Pionless Halo Effective Theory
论文作者
论文摘要
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 low-energy universality.在这里，我们通过消除排斥的旋转旋转$ξ^ - n $子系统来求助于对三体系统的简单猜测，同时保留了主要有吸引力的（可能是绑定的）旋转旋转$ξ^{ - } n $和虚拟型号spinlet spinlet $ nn $ nn $ sip-system。特别是，通过在类似FADDEEV的类似耦合的积分方程中引入尖锐的动量（紫外线）截止性参数$λ_c$，表明类似于重量级化的缩放行为，类似于重量化组的限制周期，从而表明efimov limitive的形式存在于单位限制（如$λ_），从而表明了efimov limition的正式存在，从而表明了一个离散的缩放行为。我们随后的非反应分析表明，三体结合能$ b_3 $敏感地取决于截止，而无需包括三体接触相互作用。此外，我们的分析重现了绑定能量的几个值$ b_3 \ sim 3-4 $ MEV，该值在现有潜在模型的背景下预测，范围内的调节器$λ_c$，$ \ sim 350-460 $ MEV。最后，基于这些模型输入的$ b_3 $，这是对范围内三体散射长度的球场估计，$ 2.6-4.9 $ fm受到我们的EFT分析的限制，表面上表现出了三体相关的普遍性质，这很可能以halo-counn-ano-councon-bound-bound-bound-bound-ano-councon-and-bound-and-bound-and-bound-and-councon-bound-and-counction $ nnnnnn $} nn $} nn $} nn $}。
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 low-energy 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 $Λ_c\to \infty$. 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 $B_3\sim 3-4$ MeV, predicted in context of existing potential models, with the regulator $Λ_c$ in the range, $\sim 350-460$ 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.
