AI 中文总结
该研究构建动量空间中$J/ψ NN$和$ϕ NN$三体系统的法捷耶夫方程，结合多种势源求解，发现$ϕ NN$三体系统存在束缚态，$J/ψ NN$系统无束缚态。
AI 中文摘要
我们构建了动量空间中$J/ψ NN$和$ϕ NN$三体系统的法捷耶夫方程。两体子系统的t矩阵通过求解利夫曼-施温格方程得到，其中核子-核子（NN）相互作用采用马尔弗利特-琼（Malfliet-Tjon）势构建。$J/ψ N$在${}^4S_{3/2}$和${}^2S_{1/2}$道的相互作用势取自HAL QCD合作组的结果；$ϕ N$在${}^4S_{3/2}$道的相互作用势同样取自HAL QCD结果，而${}^2S_{1/2}$道的$ϕ N$相互作用则结合了$ϕ p$关联函数分析、HAL QCD结果，以及$ϕ N$与$J/ψ N$相互作用的自旋-自旋部分与各自强子质量成反比的假设得到。求解法捷耶夫方程以寻找$J/ψ NN$和$ϕ NN$三体系统的束缚态，数值结果表明：$ϕ NN$三体系统存在束缚态，而$J/ψ NN$系统无束缚态。
英文摘要
We construct Faddeev equations for the $J/ψ\,NN$ and $ϕ\,NN$ three-body systems in momentum space. The two-body subsystem $t$-matrix is obtained by solving the Lippmann-Schwinger equations. The $NN$ interactions are constructed using the Malfliet-Tjon potential. The $J/ψ\,N$ interaction potentials in the ${}^4S_{3/2}$ and ${}^2S_{1/2}$ channels are taken from HAL QCD. The $ϕ\,N$ interaction potential in the ${}^4S_{3/2}$ channel is also taken from HAL QCD. The ${}^2S_{1/2}$ $ϕN$ interaction is obtained from the combination of the $ϕp$ correlation function analysis and the HAL QCD results, as well as from the assumption that the spin-spin parts of the $ϕN$ and $J/ψN$ interactions are inversely proportional to the respective hadron masses. The Faddeev equations are solved to find bound states in the $J/ψ\,NN$ and $ϕ\,NN$ three-body systems. The numerical results suggest that there exist bound states in the $ϕ\,NN$ three-body system, while there is no bound state in the $J/ψ\,NN$ system.
