λ-ρ mode mixing and radial Regge trajectories for triply heavy baryons Ωccc and Ωbbb in the diquark picture
Abstract
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 Ωccc and Ωbbb, 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 JP=(3/2)+ radially-excited S-wave states and construct mixed-mode Regge trajectory formulas for these symmetrized states. Unlike triply heavy baryons Ωccb/Ωcbb 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 Ωccc and Ωbbb 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∼ x2/3 (where x=nr, Nr, nr+Nr). Radially excited masses are crudely estimated via the mixed-mode Regge trajectories, which show reasonable agreement with existing theoretical predictions.
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BibTeX
@misc{chen2026λρ,
title = {{$λ$-$ρ$ mode mixing and radial Regge trajectories for triply heavy baryons $Ω_ccc$ and $Ω_bbb$ in the diquark picture}},
author = {Jiao-Kai Chen and Xin-Ru Liu and Qi Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07053},
eprint = {2610.07053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07053},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - λ-ρ mode mixing and radial Regge trajectories for triply heavy baryons Ω_ccc and Ω_bbb in the diquark picture
AU - Jiao-Kai Chen
AU - Xin-Ru Liu
AU - Qi Liu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07053
UR - https://arxiv.org/abs/2610.07053
AB - 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∼ 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.
ER -