- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Triply heavy baryon spectroscopy revisited

Hao Zhou1,2,3, Si-Qiang Luo1,2,3,*, and Xiang Liu1,2,4,3,†

  • 1School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
  • 2Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • 3Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
  • 4MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China

  • *Contact author: luosq15@lzu.edu.cn
  • †Contact author: xiangliu@lzu.edu.cn
PDF

Phys. Rev. D 112, 074007 – Published 8 October, 2025

DOI: https://doi.org/10.1103/jhr1-ccsw

Abstract

We present a comprehensive study of triply heavy baryons (Ωccc, Ωbbb, Ωbcc, and Ωbbc) within the nonrelativistic quark model, employing the Gaussian expansion method to calculate mass spectra up to D-wave states. Our analysis represents the most complete treatment to date for this model, incorporating full angular momentum mixing effects. While our predictions for low-lying states agree well with lattice quantum chromodynamics (QCD) results, we find systematically lower masses for excited states compared to lattice calculations. Using the obtained wave functions, we estimate radiative decay widths up to 1D states, revealing significant differences from previous theoretical work. Additionally, we identify and resolve several misconceptions in prior treatments of triply heavy baryon spectroscopy, particularly symmetry constraint and wave function construction in three-quark systems. These results provide crucial information for future experimental searches and theoretical investigations of triply heavy baryon systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. X. Liu, An overview of XYZ new particles, Chin. Sci. Bull. 59, 3815 (2014).
  2. A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. Yasui, Exotic hadrons with heavy flavors: X, Y, Z, and related states, Prog. Theor. Exp. Phys. 2016, 062C01 (2016).
  3. H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
  4. J.-M. Richard, Exotic hadrons: Review and perspectives, Few-Body Syst. 57, 1185 (2016).
  5. S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
  6. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
  7. Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
  8. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The XYZ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
  9. L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rep. 1019, 1 (2023).
  10. H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2023).
  11. R. Aaij et al. (LHCb Collaboration), First observation of the doubly charmed baryon decay Ξcc++→Ξc+π+, Phys. Rev. Lett. 121, 162002 (2018).
  12. P. Hasenfratz, R. R. Horgan, J. Kuti, and J. M. Richard, Heavy baryon spectroscopy in the QCD bag model, Phys. Lett. 94B, 401 (1980).
  13. A. Bernotas and V. Simonis, Heavy hadron spectroscopy and the bag model, Lith. J. Phys. 49, 19 (2009).
  14. B. Silvestre-Brac, Spectrum and static properties of heavy baryons, Few-Body Syst. 20, 1 (1996).
  15. J. Vijande, H. Garcilazo, A. Valcarce, and F. Fernandez, Spectroscopy of doubly charmed baryons, Phys. Rev. D 70, 054022 (2004).
  16. S. Migura, D. Merten, B. Metsch, and H.-R. Petry, Charmed baryons in a relativistic quark model, Eur. Phys. J. A 28, 41 (2006).
  17. Y. Jia, Variational study of weakly coupled triply heavy baryons, J. High Energy Phys. 10 (2006) 073.
  18. A. P. Martynenko, Ground-state triply and doubly heavy baryons in a relativistic three-quark model, Phys. Lett. B 663, 317 (2008).
  19. W. Roberts and M. Pervin, Heavy baryons in a quark model, Int. J. Mod. Phys. A 23, 2817 (2008).
  20. B. Patel, A. Majethiya, and P. C. Vinodkumar, Masses and magnetic moments of triply heavy flavour baryons in hypercentral model, Pramana 72, 679 (2009).
  21. J. M. Flynn, E. Hernandez, and J. Nieves, Triply heavy baryons and heavy quark spin symmetry, Phys. Rev. D 85, 014012 (2012).
  22. Z. Shah and A. K. Rai, Masses and regge trajectories of triply heavy Ωccc and Ωbbb baryons, Eur. Phys. J. A 53, 195 (2017).
  23. X.-Z. Weng, X.-L. Chen, and W.-Z. Deng, Masses of doubly heavy-quark baryons in an extended chromomagnetic model, Phys. Rev. D 97, 054008 (2018).
  24. S.-X. Qin, C. D. Roberts, and S. M. Schmidt, Poincaré-covariant analysis of heavy-quark baryons, Phys. Rev. D 97, 114017 (2018).
  25. G. Yang, J. Ping, P. G. Ortega, and J. Segovia, Triply heavy baryons in the constituent quark model, Chin. Phys. C 44, 023102 (2020).
  26. M.-S. Liu, Q.-F. Lü, and X.-H. Zhong, Triply charmed and bottom baryons in a constituent quark model, Phys. Rev. D 101, 074031 (2020).
  27. R. N. Faustov and V. O. Galkin, Triply heavy baryon spectroscopy in the relativistic quark model, Phys. Rev. D 105, 014013 (2022).
  28. E. Ortiz-Pacheco and R. Bijker, Masses and radiative decay widths of S- and P-wave singly, doubly, and triply heavy charm and bottom baryons, Phys. Rev. D 108, 054014 (2023).
  29. G.-L. Yu, Z.-Y. Li, Z.-G. Wang, and Z. Zhou, Systematic analysis of the mass spectra of triply heavy baryons, Eur. Phys. J. C 85, 543 (2025).
  30. N. S. Dhindsa, D. Chakraborty, A. Radhakrishnan, N. Mathur, and M. Padmanath, Precise study of triply charmed baryons (Ωccc), arXiv:2411.12729.
  31. M. Padmanath, R. G. Edwards, N. Mathur, and M. Peardon, Spectroscopy of triply-charmed baryons from lattice QCD, Phys. Rev. D 90, 074504 (2014).
  32. N. Mathur, M. Padmanath, and S. Mondal, Precise predictions of charmed-bottom hadrons from lattice QCD, Phys. Rev. Lett. 121, 202002 (2018).
  33. Z. S. Brown, W. Detmold, S. Meinel, and K. Orginos, Charmed bottom baryon spectroscopy from lattice QCD, Phys. Rev. D 90, 094507 (2014).
  34. T. Burch, Heavy hadrons on Nf=2 and 2+1 improved clover-Wilson lattices, arXiv:1502.00675.
  35. S. Meinel, Prediction of the Ωbbb mass from lattice QCD, Phys. Rev. D 82, 114514 (2010).
  36. S. Meinel, Excited-state spectroscopy of triply-bottom baryons from lattice QCD, Phys. Rev. D 85, 114510 (2012).
  37. C. Alexandrou, S. Bacchio, G. Christou, and J. Finkenrath, Low-lying baryon masses using twisted mass fermions ensembles at the physical pion mass, Phys. Rev. D 108, 094510 (2023).
  38. J.-B. Li, L.-C. Gui, W. Sun, J. Liang, and W. Qin, Triply charmed baryons mass decomposition from lattice QCD, Chin. Phys. C 49, 063103 (2025).
  39. Y. Lyu, H. Tong, T. Sugiura, S. Aoki, T. Doi, T. Hatsuda, J. Meng, and T. Miyamoto, Dibaryon with highest charm number near unitarity from lattice QCD, Phys. Rev. Lett. 127, 072003 (2021).
  40. H. Bahtiyar, K. U. Can, G. Erkol, P. Gubler, M. Oka, and T. T. Takahashi, Charmed baryon spectrum from lattice QCD near the physical point, Phys. Rev. D 102, 054513 (2020).
  41. C. Alexandrou and C. Kallidonis, Low-lying baryon masses using Nf=2 twisted mass clover-improved fermions directly at the physical pion mass, Phys. Rev. D 96, 034511 (2017).
  42. Y.-C. Chen and T.-W. Chiu (TWQCD Collaboration), Lattice QCD with Nf=2+1+1 domain-wall quarks, Phys. Lett. B 767, 193 (2017).
  43. K. U. Can, G. Erkol, M. Oka, and T. T. Takahashi, Look inside charmed-strange baryons from lattice QCD, Phys. Rev. D 92, 114515 (2015).
  44. C. Alexandrou, V. Drach, K. Jansen, C. Kallidonis, and G. Koutsou, Baryon spectrum with Nf=2+1+1 twisted mass fermions, Phys. Rev. D 90, 074501 (2014).
  45. Y. Namekawa et al. (PACS-CS Collaboration), Charmed baryons at the physical point in 2+1 flavor lattice QCD, Phys. Rev. D 87, 094512 (2013).
  46. S. Durr, G. Koutsou, and T. Lippert, Meson and baryon dispersion relations with Brillouin fermions, Phys. Rev. D 86, 114514 (2012).
  47. C. Alexandrou, J. Carbonell, D. Christaras, V. Drach, M. Gravina, and M. Papinutto, Strange and charm baryon masses with two flavors of dynamical twisted mass fermions, Phys. Rev. D 86, 114501 (2012).
  48. R. A. Briceno, H.-W. Lin, and D. R. Bolton, Charmed-baryon spectroscopy from lattice QCD with Nf=2+1+1 flavors, Phys. Rev. D 86, 094504 (2012).
  49. T.-W. Chiu and T.-H. Hsieh, Baryon masses in lattice QCD with exact chiral symmetry, Nucl. Phys. A755, 471 (2005).
  50. N. Brambilla, A. Vairo, and T. Rosch, Effective field theory Lagrangians for baryons with two and three heavy quarks, Phys. Rev. D 72, 034021 (2005).
  51. F. J. Llanes-Estrada, O. I. Pavlova, and R. Williams, A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential, Eur. Phys. J. C 72, 2019 (2012).
  52. J.-R. Zhang and M.-Q. Huang, Deciphering triply heavy baryons in terms of QCD sum rules, Phys. Lett. B 674, 28 (2009).
  53. Z.-G. Wang, Analysis of the triply heavy baryon states with QCD sum rules, Commun. Theor. Phys. 58, 723 (2012).
  54. T. M. Aliev, K. Azizi, and M. Savci, Masses and residues of the triply heavy spin-1/2 baryons, J. High Energy Phys. 04 (2013) 042.
  55. T. M. Aliev, K. Azizi, and M. Savc𝚤, Properties of triply heavy spin-3/2 baryons, J. Phys. G 41, 065003 (2014).
  56. K. Azizi, T. M. Aliev, and M. Savci, Properties of doubly and triply heavy baryons, J. Phys. Conf. Ser. 556, 012016 (2014).
  57. Z.-G. Wang, Analysis of the triply-heavy baryon states with the QCD sum rules, AAPPS Bull. 31, 5 (2021).
  58. Z. R. Najjar and K. Azizi, Investigation of triply heavy spin-3/2 baryons in their ground and excited states, arXiv:2504.06822.
  59. X.-H. Guo, K.-W. Wei, and X.-H. Wu, Some mass relations for mesons and baryons in Regge phenomenology, Phys. Rev. D 78, 056005 (2008).
  60. K.-W. Wei, B. Chen, and X.-H. Guo, Masses of doubly and triply charmed baryons, Phys. Rev. D 92, 076008 (2015).
  61. K.-W. Wei, B. Chen, N. Liu, Q.-Q. Wang, and X.-H. Guo, Spectroscopy of singly, doubly, and triply bottom baryons, Phys. Rev. D 95, 116005 (2017).
  62. K. Serafin, M. Gómez-Rocha, J. More, and S. D. Głazek, Approximate Hamiltonian for baryons in heavy-flavor QCD, Eur. Phys. J. C 78, 964 (2018).
  63. P.-L. Yin, C. Chen, G. a. Krein, C. D. Roberts, J. Segovia, and S.-S. Xu, Masses of ground-state mesons and baryons, including those with heavy quarks, Phys. Rev. D 100, 034008 (2019).
  64. L. X. Gutiérrez-Guerrero, A. Bashir, M. A. Bedolla, and E. Santopinto, Masses of light and heavy mesons and baryons: A unified picture, Phys. Rev. D 100, 114032 (2019).
  65. M. Gómez-Rocha, J. More, and K. Serafin, Baryon masses estimate in heavy flavor QCD: An effective particle approach to hadron spectra, Few-Body Syst. 64, 44 (2023).
  66. S.-Q. Luo and X. Liu, Newly observed Ωc(3327): A good candidate for a D-wave charmed baryon, Phys. Rev. D 107, 074041 (2023).
  67. S.-Q. Luo and X. Liu, Investigating the spectroscopy behavior of undetected 1F-wave charmed baryons, Phys. Rev. D 108, 034002 (2023).
  68. Y.-X. Peng, S.-Q. Luo, and X. Liu, Refining radiative decay studies in singly heavy baryons, Phys. Rev. D 110, 074034 (2024).
  69. S.-Q. Luo and X. Liu, Identifying triple-strangeness Ω hyperons in light of recent experimental results, Phys. Rev. D 112, 014047 (2025).
  70. S.-Q. Luo, B. Chen, X. Liu, and T. Matsuki, Predicting a new resonance as charmed-strange baryonic analog of Ds0*(2317), Phys. Rev. D 103, 074027 (2021).
  71. M. Kamimura, Nonadiabatic coupled-rearrangement-channel approach to muonic molecules, Phys. Rev. A 38, 621 (1988).
  72. E. Hiyama, Y. Kino, and M. Kamimura, Gaussian expansion method for few-body systems, Prog. Part. Nucl. Phys. 51, 223 (2003).
  73. E. Hiyama, Gaussian expansion method for few-body systems and its applications to atomic and nuclear physics, Prog. Theor. Exp. Phys. 2012, 01A204 (2012).
  74. T. Yoshida, E. Hiyama, A. Hosaka, M. Oka, and K. Sadato, Spectrum of heavy baryons in the quark model, Phys. Rev. D 92, 114029 (2015).
  75. W.-J. Deng, L.-Y. Xiao, L.-C. Gui, and X.-H. Zhong, Radiative transitions of charmonium states in a constituent quark model, arXiv:1510.08269.
  76. W.-J. Deng, H. Liu, L.-C. Gui, and X.-H. Zhong, Charmonium spectrum and their electromagnetic transitions with higher multipole contributions, Phys. Rev. D 95, 034026 (2017).
  77. W.-J. Deng, H. Liu, L.-C. Gui, and X.-H. Zhong, Spectrum and electromagnetic transitions of bottomonium, Phys. Rev. D 95, 074002 (2017).
  78. S. Capstick and N. Isgur, Baryons in a relativized quark model with chromodynamics, Phys. Rev. D 34, 2809 (1986).
  79. S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
  80. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).

Outline

Information

Phys. Rev. D 112, 074007– Published 8 October, 2025
  • Received 18 July 2025
  • Accepted 8 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation