- 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

Chiral extrapolation of the doubly charmed baryons magnetic properties

Jiong-Jiong Liu1,2,3, Zhan-Wei Liu1,2,3,*, Xiu-Lei Ren4,5,†, and Yu Zhuge1,2,3

  • 1School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
  • 2Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
  • 3Lanzhou Center for Theoretical Physics, MoE Frontiers Science Center for Rare Isotopes, Key Laboratory of Quantum Theory and Applications of MoE, Key Laboratory of Theoretical Physics of Gansu Province, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • 4School of Nuclear Science, Energy and Power Engineering, Shandong University, Jinan 250061, China
  • 5Helmholtz Institut Mainz, D-55099 Mainz, Germany

  • *Contact author: liuzhanwei@lzu.edu.cn
  • †Contact author: xiulei.ren@uni-mainz.de
PDF

Phys. Rev. D 111, 114038 – Published 30 June, 2025

DOI: https://doi.org/10.1103/gknb-p56r

Abstract

The magnetic moments, magnetic form factors, and transition magnetic form factors of doubly charmed baryons are studied within heavy baryon chiral perturbation theory. We regulate the loop integrals using the finite-range regularization. The contributions of vector mesons are taken into account to investigate the dependence of form factors on the transferred momentum. The finite volume and lattice spacing effects are considered to analyze the lattice QCD simulations which can be understood well in our framework.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (116)

  1. A. Ocherashvili et al. (SELEX Collaboration), Confirmation of the double charm baryon Ξcc+(3520) via its decay to pD+K−, Phys. Lett. B 628, 18 (2005).
  2. R. Aaij et al. (LHCb Collaboration), Precision measurement of the Ξcc++ mass, J. High Energy Phys. 02 (2020) 049.
  3. R. Aaij et al. (LHCb Collaboration), First observation of the doubly charmed baryon decay Ξcc++→Ξc+π+, Phys. Rev. Lett. 121, 162002 (2018).
  4. S. P. Ratti, New results on c-baryons and a search for cc-baryons in FOCUS, Nucl. Phys. B, Proc. Suppl. 115, 33 (2003).
  5. B. Aubert et al. (BABAR Collaboration), Search for doubly charmed baryons Ξcc+ and Ξcc++ in BABAR, Phys. Rev. D 74, 011103 (2006).
  6. R. Aaij et al. (LHCb Collaboration), Search for the doubly charmed baryon Ξcc+ in the Ξc+π−π+ final state, J. High Energy Phys. 12 (2021) 107.
  7. R. Chistov et al. (Belle Collaboration), Observation of new states decaying into Λc+K−π+ and Λc+KS0π−, Phys. Rev. Lett. 97, 162001 (2006).
  8. R. Aaij et al. (LHCb Collaboration), Measurement of the lifetime of the doubly charmed baryon Ξcc++, Phys. Rev. Lett. 121, 052002 (2018).
  9. R. Aaij et al. (LHCb Collaboration), Measurement of Ξcc++ production in pp collisions at s=13  TeV, Chin. Phys. C 44, 022001 (2020).
  10. R. Aaij et al. (LHCb Collaboration), Observation of the doubly charmed baryon decay Ξcc++→Ξc′+π+, J. High Energy Phys. 05 (2022) 038.
  11. R. Aaij et al. (LHCb Collaboration), A search for Ξcc++→D+pK−π+ decays, J. High Energy Phys. 10 (2019) 124.
  12. R. Aaij et al. (LHCb Collaboration), Search for the doubly charmed baryon Ωcc+, Sci. China Phys. Mech. Astron. 64, 101062 (2021).
  13. M. Mattson et al. (SELEX Collaboration), First observation of the doubly charmed baryon Ξcc+, Phys. Rev. Lett. 89, 112001 (2002).
  14. R. Aaij et al. (LHCb Collaboration), Observation of the doubly charmed baryon Ξcc++, Phys. Rev. Lett. 119, 112001 (2017).
  15. Z. G. Wang, Analysis of the doubly heavy baryon states and pentaquark states with QCD sum rules, Eur. Phys. J. C 78, 826 (2018).
  16. G. L. Yu, Z. Y. Li, Z. G. Wang, J. Lu, and M. Yan, Systematic analysis of doubly charmed baryons Ξcc and Ωcc, Eur. Phys. J. A 59, 126 (2023).
  17. M. Shekari Tousi and K. Azizi, Properties of doubly heavy spin-12 baryons: The ground and excited states, Phys. Rev. D 109, 054005 (2024).
  18. T. M. Aliev, K. Azizi, and M. Savci, Doubly heavy spin–1/2 baryon spectrum in QCD, Nucl. Phys. A895, 59 (2012).
  19. T. M. Aliev, K. Azizi, and M. Savci, The masses and residues of doubly heavy spin-3/2 baryons, J. Phys. G 40, 065003 (2013).
  20. Z. G. Wang, Analysis of the 1/2− and 3/2− heavy and doubly heavy baryon states with QCD sum rules, Eur. Phys. J. A 47, 81 (2011).
  21. W. F. Wang, A. Feijoo, J. Song, and E. Oset, Molecular Ωcc, Ωbb, and Ωbc states, Phys. Rev. D 106, 116004 (2022).
  22. D. L. Yao, Masses and sigma terms of doubly charmed baryons up to O(p4) in manifestly Lorentz-invariant baryon chiral perturbation theory, Phys. Rev. D 97, 034012 (2018).
  23. D. B. Lichtenberg, Magnetic moments of charmed baryons in the quark model, Phys. Rev. D 15, 345 (1977).
  24. B. Julia-Diaz and D. O. Riska, Baryon magnetic moments in relativistic quark models, Nucl. Phys. A739, 69 (2004).
  25. A. Faessler, T. Gutsche, M. A. Ivanov, J. G. Korner, V. E. Lyubovitskij, D. Nicmorus, and K. Pumsa-ard, Magnetic moments of heavy baryons in the relativistic three-quark model, Phys. Rev. D 73, 094013 (2006).
  26. S. N. Jena and D. P. Rath, Magnetic moments of light, charmed and B flavored baryons in a relativistic logarithmic potential, Phys. Rev. D 34, 196 (1986).
  27. B. Patel, A. K. Rai, and P. C. Vinodkumar, Masses and magnetic moments of charmed baryons using hyper central model, arXiv:0803.0221.
  28. C. Albertus, E. Hernandez, J. Nieves, and J. M. Verde-Velasco, Static properties and semileptonic decays of doubly heavy baryons in a nonrelativistic quark model, Eur. Phys. J. A 32, 183 (2007); 36, 119(E) (2008).
  29. Z. Shah, A. Kakadiya, K. Gandhi, and A. K. Rai, Properties of doubly heavy baryons, Universe 7, 337 (2021).
  30. B. J. Lai, F. L. Wang, and X. Liu, Investigating the M1 radiative decay behaviors and the magnetic moments of the predicted triple-charm molecular-type pentaquarks, Phys. Rev. D 109, 054036 (2024).
  31. R. Patel and M. Shah, Magnetic moment and decay properties of Ξcc++ baryon in relativistic Dirac formalism with independent quark model, DAE Symp. Nucl. Phys. 67, 947 (2024).
  32. N. Sharma, H. Dahiya, P. K. Chatley, and M. Gupta, Spin 12+, spin 32+ and transition magnetic moments of low lying and charmed baryons, Phys. Rev. D 81, 073001 (2010).
  33. Z. Shah and A. K. Rai, Excited state mass spectra of doubly heavy Ξ baryons, Eur. Phys. J. C 77, 129 (2017).
  34. A. Majethiya, B. Patel, A. K. Rai, and P. C. Vinodkumar, Properties of doubly charmed baryons in the quark-diquark model, arXiv:0809.4910.
  35. B. Silvestre-Brac, Spectrum and static properties of heavy baryons, Few-Body Syst. 20, 1 (1996).
  36. H. Mutuk, The status of Ξcc++ baryon: Investigating quark–diquark model, Eur. Phys. J. Plus 137, 10 (2022).
  37. M. Shah, R. Patel, and P. C. Vinodkumar, Radial excitation of Ωcc baryon using relativistic formalism, Few-Body Syst. 64, 34 (2023).
  38. Z. Shah, K. Thakkar, and A. K. Rai, Excited state mass spectra of doubly heavy baryons Ωcc, Ωbb and Ωbc, Eur. Phys. J. C 76, 530 (2016).
  39. N. Barik and M. Das, Magnetic moments of confined quark and baryons in an independent quark model based on Dirac quark with power law potential, Phys. Rev. D 28, 2823 (1983).
  40. H. Dahiya, N. Sharma, and P. K. Chatley, Magnetic moments of spin 12+ and spin 32+ charmed baryons, AIP Conf. Proc. 1257, 395 (2010).
  41. S. Rahmani, H. Hassanabadi, and H. Sobhani, Mass and decay properties of double heavy baryons with a phenomenological potential model, Eur. Phys. J. C 80, 312 (2020).
  42. A. Bernotas and V. Simonis, Magnetic moments of heavy baryons in the bag model reexamined, arXiv:1209.2900.
  43. S. K. Bose and L. P. Singh, Magnetic moments of charmed and B flavored hadrons in MIT bag model, Phys. Rev. D 22, 773 (1980).
  44. V. Simonis, Improved predictions for magnetic moments and M1 decay widths of heavy hadrons, arXiv:1803.01809.
  45. W. X. Zhang, H. Xu, and D. Jia, Masses and magnetic moments of hadrons with one and two open heavy quarks: Heavy baryons and tetraquarks, Phys. Rev. D 104, 114011 (2021).
  46. Y. s. Oh, D. P. Min, M. Rho, and N. N. Scoccola, Massive quark baryons as skyrmions: Magnetic moments, Nucl. Phys. A534, 493 (1991).
  47. U. Özdem, Magnetic moments of doubly heavy baryons in light-cone QCD, J. Phys. G 46, 035003 (2019).
  48. R. Dhir and R. C. Verma, Magnetic moments of (JP=3/2+) heavy baryons using effective mass scheme, Eur. Phys. J. A 42, 243 (2009).
  49. B. Mohan, T. M. S., A. Hazra, and R. Dhir, Screening of the quark charge and mixing effects on transition moments and M1 decay widths of baryons, Phys. Rev. D 106, 113007 (2022).
  50. A. Hazra, S. Rakshit, and R. Dhir, Radiative M1 transitions of heavy baryons: Effective quark mass scheme, Phys. Rev. D 104, 053002 (2021).
  51. S. Kumar, R. Dhir, and R. C. Verma, Magnetic moments of charm baryons using effective mass and screened charge of quarks, J. Phys. G 31, 141 (2005).
  52. A. N. Gadaria, N. R. Soni, and J. N. Pandya, Masses and magnetic moment of doubly heavy baryons, DAE Symp. Nucl. Phys. 61, 698 (2016).
  53. R. H. Hackman, N. G. Deshpande, D. A. Dicus, and V. L. Teplitz, M1 transitions in the MIT bag model, Phys. Rev. D 18, 2537 (1978).
  54. A. Bernotas and V. Šimonis, Radiative M1 transitions of heavy baryons in the bag model, Phys. Rev. D 87, 074016 (2013).
  55. E.-L. Cui, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Suggested search for doubly charmed baryons of JP=3/2+ via their electromagnetic transitions, Phys. Rev. D 97, 034018 (2018).
  56. T. M. Aliev, T. Barakat, and K. Şimşek, Strong BQQ′*BQQ′V vertices and the radiative decays of BQQ*→BQQγ in the light-cone sum rules, Eur. Phys. J. A 57, 160 (2021).
  57. T. Aliyev and S. Bilmiş, Properties of doubly heavy baryons in QCD, Turk. J. Phys. 46, 1 (2022).
  58. T. M. Aliev, E. Askan, and A. Ozpineci, Radiative decays of the spin-3/2 to spin-1/2 doubly heavy baryons in QCD, Phys. Rev. D 108, 054015 (2023).
  59. N. Soni and J. Pandya, Masses and radiative decay of Ωcc+ baryon, DAE Symp. Nucl. Phys. 62, 770 (2017).
  60. A. N. Gadaria, N. R. Soni, R. Chaturvedi, A. Kumar Rai, and J. N. Pandya, Decay properties of Ξcc++ baryon, DAE Symp. Nucl. Phys. 63, 912 (2018).
  61. Q. F. Lü, K. L. Wang, L. Y. Xiao, and X. H. Zhong, Mass spectra and radiative transitions of doubly heavy baryons in a relativized quark model, Phys. Rev. D 96, 114006 (2017).
  62. T. Branz, A. Faessler, T. Gutsche, M. A. Ivanov, J. G. Korner, V. E. Lyubovitskij, and B. Oexl, Radiative decays of double heavy baryons in a relativistic constituent three–quark model including hyperfine mixing, Phys. Rev. D 81, 114036 (2010).
  63. L. Y. Xiao, K. L. Wang, Q. f. Lu, X. H. Zhong, and S. L. Zhu, Strong and radiative decays of the doubly charmed baryons, Phys. Rev. D 96, 094005 (2017).
  64. H. S. Li, L. Meng, Z. W. Liu, and S. L. Zhu, Radiative decays of the doubly charmed baryons in chiral perturbation theory, Phys. Lett. B 777, 169 (2018).
  65. H. S. Li, L. Meng, Z. W. Liu, and S. L. Zhu, Magnetic moments of the doubly charmed and bottom baryons, Phys. Rev. D 96, 076011 (2017).
  66. H. S. Li and W. L. Yang, Spin-32 doubly charmed baryon contribution to the magnetic moments of the spin-12 doubly charmed baryons, Phys. Rev. D 103, 056024 (2021).
  67. K. U. Can, G. Erkol, B. Isildak, M. Oka, and T. T. Takahashi, Electromagnetic structure of charmed baryons in lattice QCD, J. High Energy Phys. 05 (2014) 125.
  68. H. Bahtiyar, Electromagnetic structure of spin-12 doubly charmed baryons in lattice QCD, Phys. Rev. D 108, 034504 (2023).
  69. K. U. Can, Lattice QCD study of the elastic and transition form factors of charmed baryons, Int. J. Mod. Phys. A 36, 2130013 (2021).
  70. H. Bahtiyar, K. U. Can, G. Erkol, M. Oka, and T. T. Takahashi, Radiative transitions of doubly charmed baryons in lattice QCD, Phys. Rev. D 98, 114505 (2018).
  71. H. Bahtiyar, K. U. Can, G. Erkol, M. Oka, and T. T. Takahashi, Radiative transitions of singly and doubly charmed baryons in lattice QCD, J. Phys. Soc. Jpn. Conf. Proc. 26, 022027 (2019).
  72. M. Z. Liu, Y. Xiao, and L. S. Geng, Magnetic moments of the spin-1/2 doubly charmed baryons in covariant baryon chiral perturbation theory, Phys. Rev. D 98, 014040 (2018).
  73. A. N. Hiller Blin, Z. F. Sun, and M. J. Vicente Vacas, Electromagnetic form factors of spin 1/2 doubly charmed baryons, Phys. Rev. D 98, 054025 (2018).
  74. J. F. Donoghue and B. R. Holstein, Improved treatment of loop diagrams in SU(3) baryon chiral perturbation theory, Phys. Lett. B 436, 331 (1998).
  75. J. F. Donoghue, B. R. Holstein, and B. Borasoy, SU(3) baryon chiral perturbation theory and long distance regularization, Phys. Rev. D 59, 036002 (1999).
  76. G. J. Wang, L. Meng, and S. L. Zhu, Radiative decays of the singly heavy baryons in chiral perturbation theory, Phys. Rev. D 99, 034021 (2019).
  77. G. C. Gellas, T. R. Hemmert, C. N. Ktorides, and G. I. Poulis, The Delta nucleon transition form-factors in chiral perturbation theory, Phys. Rev. D 60, 054022 (1999).
  78. T. A. Gail and T. R. Hemmert, Signatures of chiral dynamics in the nucleon to delta transition, Eur. Phys. J. A 28, 91 (2006).
  79. A. Faessler, T. Gutsche, B. R. Holstein, V. E. Lyubovitskij, D. Nicmorus, and K. Pumsa-ard, Light baryon magnetic moments and N→Δγ transition in a Lorentz covariant chiral quark approach, Phys. Rev. D 74, 074010 (2006).
  80. D. Arndt and B. C. Tiburzi, Baryon decuplet to octet electromagnetic transitions in quenched and partially quenched chiral perturbation theory, Phys. Rev. D 69, 014501 (2004).
  81. H. S. Li, Z. W. Liu, X. L. Chen, W. Z. Deng, and S. L. Zhu, Decuplet to octet baryon transitions in chiral perturbation theory, Eur. Phys. J. C 79, 66 (2019).
  82. S. Scherer, Introduction to chiral perturbation theory, Adv. Nucl. Phys. 27, 277 (2003).
  83. Z. R. Liang, P. C. Qiu, and D. L. Yao, One-loop analysis of the interactions between doubly charmed baryons and Nambu-Goldstone bosons, J. High Energy Phys. 07 (2023) 124.
  84. P. C. Qiu and D. L. Yao, Chiral effective Lagrangian for doubly charmed baryons up to O(q4), Phys. Rev. D 103, 034006 (2021).
  85. W. Rarita and J. Schwinger, On a theory of particles with half integral spin, Phys. Rev. 60, 61 (1941).
  86. B. Borasoy and U. G. Meissner, Chiral Lagrangians for baryons coupled to massive spin 1 fields, Int. J. Mod. Phys. A 11, 5183 (1996).
  87. A. F. Falk, Hadrons of arbitrary spin in the heavy quark effective theory, Nucl. Phys. B378, 79 (1992).
  88. L. Meng and S. L. Zhu, Light pseudoscalar meson and doubly charmed baryon scattering lengths with heavy diquark-antiquark symmetry, Phys. Rev. D 100, 014006 (2019).
  89. Z. F. Sun and M. J. Vicente Vacas, Masses of doubly charmed baryons in the extended on-mass-shell renormalization scheme, Phys. Rev. D 93, 094002 (2016).
  90. I. C. Cloet, D. B. Leinweber, and A. W. Thomas, Delta baryon magnetic moments from lattice QCD, Phys. Lett. B 563, 157 (2003).
  91. Z. R. Liang and D. L. Yao, A unified formulation of one-loop tensor integrals for finite volume effects, J. High Energy Phys. 12 (2022) 029.
  92. Y. Li, J. J. Wu, C. D. Abell, D. B. Leinweber, and A. W. Thomas, Partial wave mixing in Hamiltonian effective field theory, Phys. Rev. D 101, 114501 (2020).
  93. X. L. Ren, L. S. Geng, and J. Meng, Baryon chiral perturbation theory with Wilson fermions up to O(a2) and discretization effects of latest nf=2+1 LQCD octet baryon masses, Eur. Phys. J. C 74, 2754 (2014).
  94. B. C. Tiburzi, Baryon masses at O(a2) in chiral perturbation theory, Nucl. Phys. A761, 232 (2005).
  95. D. Arndt and B. C. Tiburzi, Hadronic electromagnetic properties at finite lattice spacing, Phys. Rev. D 69, 114503 (2004).
  96. O. Bar, G. Rupak, and N. Shoresh, Chiral perturbation theory at O(a2) for lattice QCD, Phys. Rev. D 70, 034508 (2004).
  97. P. Wang, D. B. Leinweber, A. W. Thomas, and R. D. Young, Chiral extrapolation of octet-baryon charge radii, Phys. Rev. D 79, 094001 (2009).
  98. Z. W. Liu and S. L. Zhu, Pseudoscalar meson and charmed baryon scattering lengths, Phys. Rev. D 86, 034009 (2012); 93, 019901(E) (2016).
  99. R. D. Young, D. B. Leinweber, and A. W. Thomas, Leading quenching effects in the proton magnetic moment, Phys. Rev. D 71, 014001 (2005).
  100. S. Aoki et al. (PACS-CS Collaboration), 2+1 flavor lattice QCD toward the physical point, Phys. Rev. D 79, 034503 (2009).
  101. P. Wang, D. B. Leinweber, A. W. Thomas, and R. D. Young, Chiral extrapolation of nucleon magnetic form factors, Phys. Rev. D 75, 073012 (2007).
  102. C. F. Perdrisat, V. Punjabi, and M. Vanderhaeghen, Nucleon electromagnetic form factors, Prog. Part. Nucl. Phys. 59, 694 (2007).
  103. P. Mergell, U. G. Meissner, and D. Drechsel, Dispersion theoretical analysis of the nucleon electromagnetic form-factors, Nucl. Phys. A596, 367 (1996).
  104. B. Kubis and U. G. Meissner, Low-energy analysis of the nucleon electromagnetic form-factors, Nucl. Phys. A679, 698 (2001).
  105. B. Kubis and U. G. Meissner, Baryon form-factors in chiral perturbation theory, Eur. Phys. J. C 18, 747 (2001).
  106. A. N. Hiller Blin, Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory, Phys. Rev. D 96, 093008 (2017).
  107. Y. Zhou, X. L. Ren, H. X. Chen, and L. S. Geng, Pseudoscalar meson and vector meson interactions and dynamically generated axial-vector mesons, Phys. Rev. D 90, 014020 (2014).
  108. I. V. Danilkin, L. I. R. Gil, and M. F. M. Lutz, Dynamical light vector mesons in low-energy scattering of Goldstone bosons, Phys. Lett. B 703, 504 (2011).
  109. X. L. Ren, Light-quark mass dependence of the Λ(1405) resonance, Phys. Lett. B 855, 138802 (2024).
  110. H. F. Jones and M. D. Scadron, Multipole γNΔ form-factors and resonant photoproduction and electroproduction, Ann. Phys. (N.Y.) 81, 1 (1973).
  111. S. Nozawa and D. B. Leinweber, Electromagnetic form-factors of spin 3/2 baryons, Phys. Rev. D 42, 3567 (1990).
  112. T. R. Hemmert, Heavy baryon chiral perturbation theory with light deltas, Report No. UMI-98-09346, University of Massachusetts, 1997.
  113. T. R. Hemmert, B. R. Holstein, and J. Kambor, Systematic 1/M expansion for spin 3/2 particles in baryon chiral perturbation theory, Phys. Lett. B 395, 89 (1997).
  114. E. E. Jenkins and A. V. Manohar, Chiral corrections to the baryon axial currents, Phys. Lett. B 259, 353 (1991).
  115. L. Meng, B. Wang, G. J. Wang, and S. L. Zhu, The hidden charm pentaquark states and ΣcD¯(*). interaction in chiral perturbation theory, Phys. Rev. D 100, 014031 (2019).
  116. B. Wang, Z. W. Liu, and X. Liu, B¯(*).B¯(*). Interactions in chiral effective field theory, Phys. Rev. D 99, 036007 (2019).

Outline

Information

Phys. Rev. D 111, 114038– Published 30 June, 2025
  • Received 27 March 2025
  • Accepted 19 June 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