发表机构
School of Physics and Electronic Engineering, Shanxi Normal University（山西师范大学物理与电子工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对三重重子 $\Omega_{ccc}$ 和 $\Omega_{bbb}$，提出在双夸克图像中通过排列对称化构造混合模式 Regge 轨迹的方法，发现纯模式轨迹消失并呈现发芽分支行为，估计的径向激发质量与理论预测相符。
AI 中文摘要
首次在双夸克图像中研究了由排列对称性强制产生的 $\lambda$-$\rho$ 模式混合所导致的混合模式轨迹。通过考虑重子的内部结构和子结构，我们提出了一种为三个全同夸克组成的重子构建混合模式 Regge 轨迹的方法。对于三重重子 $\Omega_{ccc}$ 和 $\Omega_{bbb}$，没有完全排列对称化的朴素双夸克-夸克基态违反了三个全同费米子所要求的泡利不相容原理的交换对称性；因此，物理本征态表现为排列对称性强制的 $\lambda$-$\rho$ 模式混合态。在最小混合假设下，我们明确地对 $J^{P}=(3/2)^{+}$ 径向激发 S 波态进行排列对称化，并为这些对称化态构建了混合模式 Regge 轨迹公式。与固定双夸克 $(cc)b/(bb)c$ 图像中的三重重子 $\Omega_{ccb}/\Omega_{cbb}$ 不同（后者存在定义明确的纯 $\rho$ 和 $\lambda$ 轨迹），对于 $\Omega_{ccc}$ 和 $\Omega_{bbb}$，由于排列驱动的交叉模式混合，真正的纯模式轨迹不再存在。由此产生的有效径向轨迹表现出一种新颖的“发芽分支”行为。原始未混合轨迹和混合模式有效轨迹均表现出 $M\sim x^{2/3}$ 的行为（其中 $x=n_r,\\,N_r,\\,n_r+N_r$）。通过混合模式 Regge 轨迹粗略估计了径向激发质量，结果与现有理论预测基本一致。
英文摘要
The mixed-mode trajectories arising from permutation-enforced $λ$-$ρ$ mode mixing are first investigated in the diquark picture. By accounting for the internal structure and substructure of baryons, we propose an approach to construct the mixed-mode Regge trajectories for baryons composed of three identical quarks. For triply heavy baryons $Ω_{ccc}$ and $Ω_{bbb}$, naive diquark-quark basis states without full permutation symmetrization violate the exchange symmetry required by the Pauli exclusion principle for three identical fermions; consequently, physical eigenstates arise as permutation-enforced $λ$-$ρ$ mode admixtures. Under the minimal-mixing assumption, we explicitly perform permutation symmetrization for the $J^{P}=(3/2)^{+}$ radially-excited S-wave states and construct mixed-mode Regge trajectory formulas for these symmetrized states. Unlike triply heavy baryons $Ω_{ccb}/Ω_{cbb}$ in the fixed diquark $(cc)b/(bb)c$ picture where well-defined pure $ρ$- and $λ$-trajectories exist, genuine pure-mode trajectories no longer survive for $Ω_{ccc}$ and $Ω_{bbb}$ due to permutation-driven cross-mode mixing. The resulting effective radial trajectories exhibit a novel sprouting-branch-like behavior. Both the original unmixed trajectories and the mixed-mode effective trajectories exhibit behavior of $M\sim x^{2/3}$ (where $x=n_r,\,N_r,\,n_r+N_r$). Radially excited masses are crudely estimated via the mixed-mode Regge trajectories, which show reasonable agreement with existing theoretical predictions.
Comments8 pages, 2 figures
