AI 中文总结
本研究通过计算$X(3872)$奇特强子的磁矩，区分其色单态与紧致内部构型，解决了三体力公式的量纲不一致问题，发现两类构型的磁矩差异可作为结构指示。
AI 中文摘要
$X(3872)$奇特强子的性质仍是强子谱学中最具争议的问题之一。我们在包含由$SU(3)_C$立方卡西米尔算符产生的三体力的非相对论夸克模型内，采用自洽的量纲分析计算其磁矩。与以往使用不受控的大耦合常数的研究不同，我们利用Noh等人（2024年）基于格点QCD和重子谱学的最新分析提取的约10–20 MeV的实际值，确定了三体力强度。\n 我们发现磁矩预测结果分为两个截然不同的区域：纯色单态构型给出的结果为$μ_X = -0.99 \pm 0.02\\,μ_N$，而紧致构型给出的结果为$μ_X = -1.17$至$-1.23\\,μ_N$。两种紧致情形之间的差异（$0.06\\,μ_N$）与模型的系统不确定性（约$0.15\\,μ_N$）相当，解读时需谨慎。然而，纯色单态与紧致情形之间的差异（约$0.18$–$0.24\\,μ_N$）大于估计的模型系统不确定性，可提供定性的结构指示。\n 我们强调，纯色单态构型是分子态的简化代理，并不代表具有大空间延展度的物理$D^0\bar{D}^{*0}$分子。完整的分子态处理需要耦合道动力学和长程π交换势，这超出了本工作的范围。\n 我们还解决了立方卡西米尔三体力公式中长期存在的量纲不一致问题，并通过详细的灵敏度和不确定性分析证明，在三体力耦合的物理相关范围内，我们的结论是稳健的。
英文摘要
The nature of the $X(3872)$ exotic hadron remains one of the most debated questions in hadron spectroscopy. We calculate its magnetic moment within a non-relativistic quark model that includes the three-body force arising from the cubic Casimir operator of $SU(3)_C$ with consistent dimensional analysis. Unlike previous works that used an uncontrolled large coupling, we fix the three-body strength using the realistic value of $\sim 10$--$20$ MeV extracted from the recent analysis of Noh et al.~(2024) based on lattice QCD and baryon spectroscopy. We find that the magnetic moment predictions fall into two distinct regions: the pure color-singlet configuration yields $μ_X = -0.99 \pm 0.02\,μ_N$, while the compact configurations yield $μ_X = -1.17$ to $-1.23\,μ_N$. The difference between the two compact scenarios ($0.06\,μ_N$) is comparable to the systematic uncertainty of the model ($\sim 0.15\,μ_N$) and should be interpreted with caution. However, the distinction between the pure color-singlet and the compact scenarios ($\sim 0.18$--$0.24\,μ_N$) is larger than the estimated model systematic uncertainty and may provide a qualitative structural indicator. We emphasize that the pure color-singlet configuration is a simplified proxy for a molecule and does not represent a physical $D^0\bar{D}^{*0}$ molecule with large spatial extent. A full molecular treatment would require coupled-channel dynamics and long-range pion-exchange potentials, which are beyond the scope of this work. We also resolve a long-standing dimensional inconsistency in the cubic Casimir three-body force formulation and demonstrate through a detailed sensitivity and uncertainty analysis that our conclusions are robust for the physically relevant range of the three-body coupling.
