λ, ρ, and σ Regge trajectories for the quadruply heavy pentaquark bbu̅cc in the diquark-triquark picture
Abstract
Systematic investigations of four series of Regge trajectories for quadruply heavy pentaquarks are still lacking. Using the diquark and triquark Regge trajectory relations, we propose the Regge trajectory relations for the quadruply heavy pentaquark bbu̅cc: M=2mb+2mc+mu+5C/2 +βxλ(xλ+c0xλ)2/3 +βxρ1(xρ1+c0xρ1)2/3+βxρ2√(xρ2+c0xρ2) +βxσ(xσ+c0xσ)2/3. Four series of Regge trajectories, namely the λ-, ρ1-, ρ2-, and σ-trajectories, are investigated. We demonstrate that accounting for the internal structure and substructure of pentaquarks is indispensable for constructing the ρ1-, ρ2-, and σ-trajectories; without such structural considerations, functional form and trajectory parameters can only be obtained via pure fitting against theoretical or experimental data. We further prove that the Regge trajectories of diquark 1, triquark, and diquark 2 (embedded within the triquark) do not correspond one-to-one to the ρ1-, ρ2-, and σ-trajectories. Nevertheless, these trajectories govern the behaviors of the respective ρ1-, ρ2-, and σ-trajectories. For both configurations (bb)(u̅(cc)) and (cc)(u̅(bb)), the λ-, ρ1-, and σ-trajectories exhibit behavior of M∼x2/3 (x=nr1,nr3,l1,l3,Nr,L), whereas the ρ2-trajectories exhibit behavior of M∼√x (x=nr2, l2). The functional behavior of Regge trajectories for diquarks and triquark offers guidance for fitting the pentaquark Regge trajectories. Additionally, we provide rough estimates for spin-averaged masses of the λ-, ρ1-, ρ2-, and σ-excited states.
Related
- λ, ρ, and σ Regge trajectories for the hexaquark (u̅(cc))(b(b̅b̅)) in the triquark-antitriquark picture
- λ-ρ mode mixing and radial Regge trajectories for triply heavy baryons Ωccc and Ωbbb in the diquark picture
- Analysis of the hidden-charm pentaquark candidates in the J/ψΩ mass spectrum via the QCD sum rules
- Scalar diquark mass and quark–diquark potential from lattice QCD using the potential method with a static quark
- Two-body strong decays of the Pcs(4338) as a hidden-charm pentaquark state via the QCD sum rules
BibTeX
@misc{liu2026regge,
title = {{$λ$, $ρ$, and $σ$ Regge trajectories for the quadruply heavy pentaquark $bb\barucc$ in the diquark-triquark picture}},
author = {Xin-Ru Liu and Qi Liu and Jiao-Kai Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10631},
eprint = {2607.10631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10631},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - λ, ρ, and σ Regge trajectories for the quadruply heavy pentaquark bbu̅cc in the diquark-triquark picture
AU - Xin-Ru Liu
AU - Qi Liu
AU - Jiao-Kai Chen
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.10631
UR - https://arxiv.org/abs/2607.10631
AB - Systematic investigations of four series of Regge trajectories for quadruply heavy pentaquarks are still lacking. Using the diquark and triquark Regge trajectory relations, we propose the Regge trajectory relations for the quadruply heavy pentaquark bbu̅cc: M=2m_b+2m_c+m_u+5C/2 +β_x_λ(x_λ+c_0x_λ)^2/3 +β_x_ρ_1(x_ρ_1+c_0x_ρ_1)^2/3+β_x_ρ_2√(x_ρ_2+c_0x_ρ_2) +β_x_σ(x_σ+c_0x_σ)^2/3. Four series of Regge trajectories, namely the λ-, ρ_1-, ρ_2-, and σ-trajectories, are investigated. We demonstrate that accounting for the internal structure and substructure of pentaquarks is indispensable for constructing the ρ_1-, ρ_2-, and σ-trajectories; without such structural considerations, functional form and trajectory parameters can only be obtained via pure fitting against theoretical or experimental data. We further prove that the Regge trajectories of diquark 1, triquark, and diquark 2 (embedded within the triquark) do not correspond one-to-one to the ρ_1-, ρ_2-, and σ-trajectories. Nevertheless, these trajectories govern the behaviors of the respective ρ_1-, ρ_2-, and σ-trajectories. For both configurations (bb)(u̅(cc)) and (cc)(u̅(bb)), the λ-, ρ_1-, and σ-trajectories exhibit behavior of M∼x^2/3 (x=n_r_1,n_r_3,l_1,l_3,N_r,L), whereas the ρ_2-trajectories exhibit behavior of M∼√x (x=n_r_2, l_2). The functional behavior of Regge trajectories for diquarks and triquark offers guidance for fitting the pentaquark Regge trajectories. Additionally, we provide rough estimates for spin-averaged masses of the λ-, ρ_1-, ρ_2-, and σ-excited states.
ER -