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Electromagnetic polarizabilities of the triplet hadrons in heavy hadron chiral perturbation theory

Hao Dang1,*, Liang-Zhen Wen1,†, Yan-Ke Chen2,‡, and Shi-Lin Zhu2,§

  • *Contact author: haodang@stu.pku.edu.cn
  • †Contact author: wenlzh_hep-th@stu.pku.edu.cn
  • ‡Contact author: chenyanke@pku.edu.cn
  • §Contact author: zhusl@pku.edu.cn

Phys. Rev. D 113, 094007 – Published 5 May, 2026

DOI: https://doi.org/10.1103/dlbl-1t6v

Abstract

We investigate the electromagnetic polarizabilities of singly heavy mesons and doubly heavy baryons within the framework of heavy hadron chiral perturbation theory up to O(p3). We estimate the low-energy constants using the nonrelativistic constituent quark model. A striking prediction of our study is the giant electric polarizabilities of the D* mesons: αE(D¯*0)≈294×10−4  fm3 and αE(D*−)≈1.42–64.5i×10−4  fm3. These anomalously large values arise from the near-degenerate mass between D* and Dπ, which are orders of magnitude larger than those of their bottom counterparts. This kinematic coincidence induces a pronounced cusp structure in the chiral loops, reflecting the long-range dynamics of a pion cloud. For doubly heavy baryons, polarizabilities depend strongly on heavy-flavor composition: the bcq system differs markedly from ccq and bbq due to mixing with scalar heavy-diquark states. Using heavy diquark–antiquark symmetry (HDAS), we unify the chiral dynamics of singly heavy mesons and doubly heavy baryons in the heavy-quark limit. The pion-loop contributions dominate the electromagnetic structure of heavy hadrons and provide essential benchmarks for future lattice QCD simulations.

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References (76)

  1. S. Weinberg, Phenomenological Lagrangians, Physica (Amsterdam) 96A, 327 (1979).
  2. E. E. Jenkins and A. V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255, 558 (1991).
  3. V. Bernard, N. Kaiser, J. Kambor, and U. G. Meissner, Chiral structure of the nucleon, Nucl. Phys. B388, 315 (1992).
  4. T. R. Hemmert, B. R. Holstein, and J. Kambor, Chiral Lagrangians and delta(1232) interactions: Formalism, J. Phys. G 24, 1831 (1998).
  5. M. A. Ivanov, V. E. Lyubovitskij, J. G. Körner, and P. Kroll, Heavy baryon transitions in a relativistic three-quark model, Phys. Rev. D 56, 348 (1997).
  6. M. A. Ivanov, J. G. Körner, V. E. Lyubovitskij, and A. G. Rusetsky, Strong and radiative decays of heavy flavored baryons, Phys. Rev. D 60, 094002 (1999).
  7. S. Tawfiq, J. G. Körner, and P. J. O’Donnell, Electromagnetic transitions of heavy baryons in the SU(2Nf)⊗o(3) symmetry, Phys. Rev. D 63, 034005 (2001).
  8. 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).
  9. A. Faessler, T. Gutsche, M. A. Ivanov, J. G. Körner, 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).
  10. 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).
  11. A. Majethiya, K. Thakkar, and P. C. Vinodkumar, Spectroscopy and decay properties of Σb, Λb baryons in quark–diquark model, Chin. J. Phys. 54, 495 (2016).
  12. K.-L. Wang, Y.-X. Yao, X.-H. Zhong, and Q. Zhao, Strong and radiative decays of the low-lying s- and p-wave singly heavy baryons, Phys. Rev. D 96, 116016 (2017).
  13. A. Hazra, S. Rakshit, and R. Dhir, Radiative m1 transitions of heavy baryons: Effective quark mass scheme, Phys. Rev. D 104, 053002 (2021).
  14. E. Sucipto and R. L. Thews, Radiative-decay systematics and flavor-symmetry breaking from heavy quarks, Phys. Rev. D 36, 2074 (1987).
  15. W. Jaus, Semileptonic, radiative, and pionic decays of B, B* and D, D* mesons, Phys. Rev. D 53, 1349 (1996); 54, 5904(E) (1996).
  16. H.-M. Choi, Decay constants and radiative decays of heavy mesons in light-front quark model, Phys. Rev. D 75, 073016 (2007).
  17. M. Priyadarsini, P. C. Dash, S. Kar, S. P. Patra, and N. Barik, Electromagnetic form factors of heavy flavored vector mesons, Phys. Rev. D 94, 113011 (2016).
  18. M. A. Ivanov and Y. M. Valit, Radiative and hadronic decays of heavy vector mesons, Z. Phys. C 67, 633 (1995).
  19. S. K. Bose and L. P. Singh, Magnetic moments of charmed and b-flavored hadrons in the mit bag model, Phys. Rev. D 22, 773 (1980).
  20. V. Simonis, Improved predictions for magnetic moments and M1 decay widths of heavy hadrons, arXiv:1803.01809.
  21. A. Bernotas and V. Simonis, Magnetic moments of heavy baryons in the bag model reexamined, Lith. J. Phys. 53, 84 (2013).
  22. A. Bernotas and V. Šimonis, Radiative m1 transitions of heavy baryons in the bag model, Phys. Rev. D 87, 074016 (2013).
  23. 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).
  24. J. L. Goity and W. Roberts, Radiative transitions in heavy mesons in a relativistic quark model, Phys. Rev. D 64, 094007 (2001).
  25. D. Ebert, R. N. Faustov, and V. O. Galkin, Radiative M1 decays of heavy light mesons in the relativistic quark model, Phys. Lett. B 537, 241 (2002).
  26. A. Agamaliev, T. Aliev, and M. Savc𝚤, Radiative decays of negative parity heavy baryons in the framework of the light cone QCD sum rules, Nucl. Phys. A958, 38 (2017).
  27. T. M. Aliev, M. Savci, and V. S. Zamiralov, Vector meson dominance and radiative decays of heavy spin-3/2 baryons to heavy spin-1/2 baryons, Mod. Phys. Lett. A 27, 1250054 (2012).
  28. T. M. Aliev, E. Iltan, and N. K. Pak, Radiative D* meson decays in QCD sum rules, Phys. Lett. B 334, 169 (1994).
  29. H. G. Dosch and S. Narison, B* B pi (gamma) couplings and D*−>D pi (gamma) decays within a 1/M expansion in full QCD, Phys. Lett. B 368, 163 (1996).
  30. S.-L. Zhu, W.-Y. P. Hwang, and Z.-s. Yang, D*—> D gamma and B*—> B gamma as derived from QCD sum rules, Mod. Phys. Lett. A 12, 3027 (1997).
  31. S.-L. Zhu, W.-Y. P. Hwang, and Z.-S. Yang, The Σc and Λc magnetic moments from QCD spectral sum rules, Phys. Rev. D 56, 7273 (1997).
  32. S.-L. Zhu and Y.-B. Dai, Radiative decays of heavy hadrons from light cone QCD sum rules in the leading order of HQET, Phys. Rev. D 59, 114015 (1999).
  33. U. Özdem, Magnetic moments of doubly heavy baryons in light-cone QCD, J. Phys. G 46, 035003 (2019).
  34. S. Scholl and H. Weigel, Magnetic moments of baryons with a single heavy quark, Nucl. Phys. A735, 163 (2004).
  35. Y.-s. Oh, D.-P. Min, M. Rho, and N. N. Scoccola, Massive quark baryons as skyrmions: Magnetic moments, Nucl. Phys. A534, 493 (1991).
  36. Y.-s. Oh and B.-Y. Park, Magnetic moments of heavy baryons in the skyrme model, Mod. Phys. Lett. A 11, 653 (1996).
  37. J.-Y. Kim, H.-C. Kim, G.-S. Yang, and M. Oka, Electromagnetic transitions of the singly charmed baryons with spin 3/2, Phys. Rev. D 103, 074025 (2021).
  38. Y.-Z. Xu, The electromagnetic form factors of heavy-light pseudo-scalar and vector mesons, J. High Energy Phys. 07 (2024) 118.
  39. H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. C. Lin, T.-M. Yan, and H.-L. Yu, Chiral Lagrangians for radiative decays of heavy hadrons, Phys. Rev. D 47, 1030 (1993).
  40. P. Cho, Strong and electromagnetic decays of two new Λc* baryons, Phys. Rev. D 50, 3295 (1994).
  41. M. J. Savage, E2 strength in the radiative charmed baryon decay Σc*—>Λc γ, Phys. Lett. B 345, 61 (1995).
  42. B. C. Tiburzi, Baryon electromagnetic properties in partially quenched heavy hadron chiral perturbation theory, Phys. Rev. D 71, 054504 (2005).
  43. N. Jiang, X.-L. Chen, and S.-L. Zhu, Electromagnetic decays of the charmed and bottom baryons in chiral perturbation theory, Phys. Rev. D 92, 054017 (2015).
  44. 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).
  45. L. Meng, H.-S. Li, Z.-W. Liu, and S.-L. Zhu, Magnetic moments of the spin-32 doubly heavy baryons, Eur. Phys. J. C 77, 869 (2017).
  46. 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).
  47. B. Wang, B. Yang, L. Meng, and S.-L. Zhu, Radiative transitions and magnetic moments of the charmed and bottom vector mesons in chiral perturbation theory, Phys. Rev. D 100, 016019 (2019).
  48. 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).
  49. G.-J. Wang, L. Meng, H.-S. Li, Z.-W. Liu, and S.-L. Zhu, Magnetic moments of the spin-12 singly charmed baryons in chiral perturbation theory, Phys. Rev. D 98, 054026 (2018).
  50. D. Becirevic and B. Haas, D*—> D pi and D*—> D gamma decays: Axial coupling and magnetic moment of D* meson, Eur. Phys. J. C 71, 1734 (2011).
  51. 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 (2013) 125.
  52. H. Bahtiyar, K. U. Can, G. Erkol, and M. Oka, Ωcγ→Ωc* transition in lattice QCD, Phys. Lett. B 747, 281 (2015).
  53. 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).
  54. H. Bahtiyar, K. U. Can, G. Erkol, M. Oka, and T. T. Takahashi, Ξcγ→Ξc′ transition in lattice QCD, Phys. Lett. B 772, 121 (2017).
  55. 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).
  56. K. U. Can, Lattice QCD study of the elastic and transition form factors of charmed baryons, Int. J. Mod. Phys. A 36, 2130013 (2021).
  57. B. R. Holstein and S. Scherer, Hadron Polarizabilities, Annu. Rev. Nucl. Part. Sci. 64, 51 (2014).
  58. T. Ericson and J. Hüfner, Low-frequency photon scattering by nuclei, Nucl. Phys. B57, 604 (1973).
  59. V. Bernard, N. Kaiser, and U.-G. Meissner, Chiral expansion of the nucleon’s electromagnetic polarizabilities, Phys. Rev. Lett. 67, 1515 (1991).
  60. V. Bernard, N. Kaiser, and U. G. Meissner, Nucleons with chiral loops: Electromagnetic polarizabilities, Nucl. Phys. B373, 346 (1992).
  61. V. Bernard, N. Kaiser, A. Schmidt, and U. G. Meissner, Consistent calculation of the nucleon electromagnetic polarizabilities in chiral perturbation theory beyond next-to-leading order, Phys. Lett. B 319, 269 (1993).
  62. V. Bernard, N. Kaiser, U. G. Meissner, and A. Schmidt, Aspects of nucleon Compton scattering, Z. Phys. A 348, 317 (1994).
  63. Y.-K. Chen, L.-Z. Wen, L. Meng, and S.-L. Zhu, Electromagnetic polarizabilities of the spin-12 singly heavy baryons in heavy baryon chiral perturbation theory, Phys. Rev. D 111, 054019 (2025).
  64. L.-Z. Wen, Y.-K. Chen, L. Meng, and S.-L. Zhu, Electromagnetic polarizabilities of the spin-32 baryons in heavy baryon chiral perturbation theory, Eur. Phys. J. C 85, 1210 (2025).
  65. M. J. Savage and M. B. Wise, Spectrum of baryons with two heavy quarks, Phys. Lett. B 248, 177 (1990).
  66. 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).
  67. E. Llanta and R. Tarrach, Pion electromagnetic polarizabilities and quarks, Phys. Lett. 91B, 132 (1980).
  68. J. Bernabeu and R. Tarrach, Long range potentials and the electromagnetic polarizabilities, Ann. Phys. (N.Y.) 102, 323 (1976).
  69. T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. C. Lin, and H.-L. Yu, Heavy-quark symmetry and chiral dynamics, Phys. Rev. D 46, 1148 (1992).
  70. Y. Ma, L. Meng, Y.-K. Chen, and S.-L. Zhu, Ground state baryons in the flux-tube three-body confinement model using diffusion Monte Carlo, Phys. Rev. D 107, 054035 (2023).
  71. S. Ahmed et al. (CLEO Collaboration), First measurement of Gamma(D*+). Phys. Rev. Lett. 87, 251801 (2001).
  72. H. Ohki, H. Matsufuru, and T. Onogi, Determination of B*B pi coupling in unquenched QCD, Phys. Rev. D 77, 094509 (2008).
  73. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  74. V. Bernard, N. Kaiser, and U.-G. Meißner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 04, 193 (1995).
  75. S. Scherer, Introduction to chiral perturbation theory, Adv. Nucl. Phys. 27, 277 (2003).
  76. T. R. Hemmert, B. R. Holstein, and J. Kambor, Δ(1232) and the polarizabilities of the nucleon, Phys. Rev. D 55, 5598 (1997).

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