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Landau-Zener-Stückelberg-Majorana dynamics of magnetized quarkonia

Ahmad Jafar Arifi1,2,* and Kei Suzuki3,†

  • *Contact author: aj.arifi01@gmail.com
  • †Contact author: k.suzuki.2010@th.phys.titech.ac.jp
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Phys. Rev. D 113, 054047 – Published 26 March, 2026

DOI: https://doi.org/10.1103/xc28-3v8r

Abstract

The mass spectrum of hadrons in magnetic fields features avoided level-crossing structures arising from the mixing of spin eigenstates. In this work, we investigate the impact of level-crossing dynamics of charmonia subjected to time-dependent magnetic fields, where we particularly focus on the occupation probabilities of two or more states as they undergo transitions at avoided crossings. Using a static spectrum of charmonia in magnetic fields, we construct a multichannel Landau-Zener Hamiltonian. Within this framework, we analyze the time evolution under several representative magnetic-field profiles, including linear ramps and Gaussian decays corresponding to single-passage dynamics, as well as Gaussian pulses realizing double-passage dynamics, and compute the occupation probabilities over a wide range of sweep rates and initial conditions. Our results show that nonadiabatic dynamics, including Landau-Zener transitions and Stückelberg interference, strongly influences the occupation probabilities of charmonia. These findings provide new insights into the real-time dynamics of magnetized hadrons and offer useful guidance for future lattice simulation studies.

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References (79)

  1. G. S. Bali, F. Bruckmann, G. Endrődi, Z. Fodor, S. D. Katz, S. Krieg, A. Schäfer, and K. K. Szabó, The QCD phase diagram for external magnetic fields, J. High Energy Phys. 02 (2012) 044.
  2. E. V. Luschevskaya and O. V. Larina, The ρ and A mesons in a strong Abelian magnetic field in SU(2) lattice gauge theory, Nucl. Phys. B884, 1 (2014).
  3. Y. Hidaka and A. Yamamoto, Charged vector mesons in a strong magnetic field, Phys. Rev. D 87, 094502 (2013).
  4. E. V. Luschevskaya, O. E. Solovjeva, O. A. Kochetkov, and O. V. Teryaev, Magnetic polarizabilities of light mesons in SU(3) lattice gauge theory, Nucl. Phys. B898, 627 (2015).
  5. E. V. Luschevskaya, O. E. Solovjeva, and O. V. Teryaev, Magnetic polarizability of pion, Phys. Lett. B 761, 393 (2016).
  6. G. S. Bali, B. B. Brandt, G. Endrődi, and B. Gläßle, Meson masses in electromagnetic fields with Wilson fermions, Phys. Rev. D 97, 034505 (2018).
  7. G. S. Bali, B. B. Brandt, G. Endrődi, and B. Gläßle, Weak decay of magnetized pions, Phys. Rev. Lett. 121, 072001 (2018).
  8. E. V. Luschevskaya, O. V. Teryaev, D. Y. Golubkov, O. V. Solovjeva, and R. A. Ishkuvatov, Tensor polarizability of the vector mesons from SU(3) lattice gauge theory, J. High Energy Phys. 11 (2018) 186.
  9. K. Hattori and A. Yamamoto, Meson deformation by magnetic fields in lattice QCD, Prog. Theor. Exp. Phys. 2019, 043B04 (2019).
  10. R. Bignell, W. Kamleh, and D. Leinweber, Pion in a uniform background magnetic field with clover fermions, Phys. Rev. D 100, 114518 (2019).
  11. R. Bignell, W. Kamleh, and D. Leinweber, Pion magnetic polarisability using the background field method, Phys. Lett. B 811, 135853 (2020).
  12. H.-T. Ding, S.-T. Li, A. Tomiya, X.-D. Wang, and Y. Zhang, Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature, Phys. Rev. D 104, 014505 (2021).
  13. H.-T. Ding, S.-T. Li, J.-H. Liu, and X.-D. Wang, Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium, Phys. Rev. D 105, 034514 (2022).
  14. H.-T. Ding, J.-B. Gu, S.-T. Li, and R. Thakkar, Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses, Phys. Rev. D 111, 074513 (2025).
  15. G. Endrődi, QCD with background electromagnetic fields on the lattice: A review, Prog. Part. Nucl. Phys. 141, 104153 (2025).
  16. M. C. Bañuls and K. Cichy, Review on novel methods for lattice gauge theories, Rep. Prog. Phys. 83, 024401 (2020).
  17. K. Marasinghe and K. Tuchin, Quarkonium dissociation in quark-gluon plasma via ionization in a magnetic field, Phys. Rev. C 84, 044908 (2011).
  18. K. Tuchin, J/ψ dissociation in parity-odd bubbles, Phys. Lett. B 705, 482 (2011).
  19. D.-L. Yang and B. Müller, J/ψ production by magnetic excitation of ηc, J. Phys. G 39, 015007 (2012).
  20. K. Tuchin, Particle production in strong electromagnetic fields in relativistic heavy-ion collisions, Adv. High Energy Phys. 2013, 490495 (2013).
  21. C. S. Machado, F. S. Navarra, E. G. de Oliveira, J. Noronha, and M. Strickland, Heavy quarkonium production in a strong magnetic field, Phys. Rev. D 88, 034009 (2013).
  22. J. Alford and M. Strickland, Charmonia and bottomonia in a magnetic field, Phys. Rev. D 88, 105017 (2013).
  23. S. Cho, K. Hattori, S. H. Lee, K. Morita, and S. Ozaki, QCD sum rules for magnetically induced mixing between ηc and J/ψ, Phys. Rev. Lett. 113, 172301 (2014).
  24. D. Dudal and T. G. Mertens, Melting of charmonium in a magnetic field from an effective AdS/QCD model, Phys. Rev. D 91, 086002 (2015).
  25. S. Cho, K. Hattori, S. H. Lee, K. Morita, and S. Ozaki, Charmonium spectroscopy in strong magnetic fields by QCD sum rules: S-wave ground states, Phys. Rev. D 91, 045025 (2015).
  26. C. Bonati, M. D’Elia, and A. Rucci, Heavy quarkonia in strong magnetic fields, Phys. Rev. D 92, 054014 (2015).
  27. A. V. Sadofyev and Y. Yin, The charmonium dissociation in an “anomalous wind”, J. High Energy Phys. 01 (2016) 052.
  28. K. Suzuki and T. Yoshida, Cigar-shaped quarkonia under strong magnetic field, Phys. Rev. D 93, 051502 (2016).
  29. T. Yoshida and K. Suzuki, Heavy meson spectroscopy under strong magnetic field, Phys. Rev. D 94, 074043 (2016).
  30. M. Hasan, B. Chatterjee, and B. K. Patra, Heavy quark potential in a static and strong homogeneous magnetic field, Eur. Phys. J. C 77, 767 (2017).
  31. B. Singh, L. Thakur, and H. Mishra, Heavy quark complex potential in a strongly magnetized hot QGP medium, Phys. Rev. D 97, 096011 (2018).
  32. N. R. F. Braga and L. F. Ferreira, Heavy meson dissociation in a plasma with magnetic fields, Phys. Lett. B 783, 186 (2018).
  33. S. Iwasaki, M. Oka, K. Suzuki, and T. Yoshida, Hadronic Paschen–Back effect, Phys. Lett. B 790, 71 (2019).
  34. Amal Jahan C. S., N. Dhale, S. Reddy P., S. Kesarwani, and A. Mishra, Charmonium states in strong magnetic fields, Phys. Rev. C 98, 065202 (2018).
  35. S. Iwasaki and K. Suzuki, Quarkonium radiative decays from the hadronic Paschen-Back effect, Phys. Rev. D 98, 054017 (2018).
  36. M. Hasan, B. K. Patra, B. Chatterjee, and P. Bagchi, Landau damping in a strong magnetic field: Dissociation of quarkonia, Nucl. Phys. A995, 121688 (2020).
  37. N. R. F. Braga and L. F. Ferreira, Quasinormal modes for quarkonium in a plasma with magnetic fields, Phys. Lett. B 795, 462 (2019).
  38. M. Hasan and B. K. Patra, Dissociation of heavy quarkonia in a weak magnetic field, Phys. Rev. D 102, 036020 (2020).
  39. J. Zhou, X. Chen, Y.-Q. Zhao, and J. Ping, Thermodynamics of heavy quarkonium in a magnetic field background, Phys. Rev. D 102, 086020 (2020).
  40. N. R. F. Braga and R. da Mata, Configuration entropy description of charmonium dissociation under the influence of magnetic fields, Phys. Lett. B 811, 135918 (2020).
  41. N. R. F. Braga, Y. F. Ferreira, and L. F. Ferreira, Configuration entropy and stability of bottomonium radial excitations in a plasma with magnetic fields, Phys. Rev. D 105, 114044 (2022).
  42. S. S. Jena, B. Shukla, D. Dudal, and S. Mahapatra, Entropic force and real-time dynamics of holographic quarkonium in a magnetic field, Phys. Rev. D 105, 086011 (2022).
  43. J. Hu, S. Shi, Z. Xu, J. Zhao, and P. Zhuang, Magnetic field induced hair structure in the charmonium gluon dissociation, Phys. Rev. D 105, 094013 (2022).
  44. R. Ghosh, A. Bandyopadhyay, I. Nilima, and S. Ghosh, Anisotropic tomography of heavy quark dissociation by using the general propagator structure in a finite magnetic field, Phys. Rev. D 106, 054010 (2022).
  45. P. Parui, S. De, A. Kumar, and A. Mishra, QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis, Phys. Rev. D 106, 114033 (2022).
  46. J. Sebastian, L. Thakur, H. Mishra, and N. Haque, Heavy quarkonia in QGP medium in an arbitrary magnetic field, Phys. Rev. D 108, 094001 (2023).
  47. I. Nilima, M. Hasan, B. K. Singh, and M. Y. Jamal, Quarkonia dissociation at finite magnetic field in the presence of momentum anisotropy, Eur. Phys. J. C 84, 160 (2024).
  48. S. S. Jena, J. Barman, B. Toniato, D. Dudal, and S. Mahapatra, A dynamical Einstein-Born-Infeld-dilaton model and holographic quarkonium melting in a magnetic field, J. High Energy Phys. 12 (2024) 096.
  49. B. Shukla, J. Nongmaithem, D. Dudal, and S. Mahapatra, Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a QQ¯ pair in holographic QCD, Phys. Rev. D 111, 106002 (2025).
  50. L. Wen, M. Li, Y. Zhou, Y. Li, and J. P. Vary, Relativistic dynamics of charmonia in strong magnetic fields, Phys. Rev. D 112, 014019 (2025).
  51. S. S. Jena, A. Bhattacharjee, D. Dudal, and S. Mahapatra, Probing quarkonium diffusion in a magnetized quark-gluon plasma, Phys. Rev. D 112, 086010 (2025).
  52. A. J. Arifi and K. Suzuki, Structure of heavy quarkonia in a strong magnetic field, Phys. Rev. D 112, 094013 (2025).
  53. C. A. Dominguez, M. Koning, and L. A. Hernández, Magnetic catalysis of charmonium in the vector channel, Phys. Rev. D 112, 094049 (2025).
  54. K. Hattori and X.-G. Huang, Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions, Nucl. Sci. Tech. 28, 26 (2017).
  55. J. Zhao, K. Zhou, S. Chen, and P. Zhuang, Heavy flavors under extreme conditions in high energy nuclear collisions, Prog. Part. Nucl. Phys. 114, 103801 (2020).
  56. S. Iwasaki, M. Oka, and K. Suzuki, A review of quarkonia under strong magnetic fields, Eur. Phys. J. A 57, 222 (2021).
  57. X. Guo, S. Shi, N. Xu, Z. Xu, and P. Zhuang, Magnetic field effect on charmonium production in high energy nuclear collisions, Phys. Lett. B 751, 215 (2015).
  58. K. Suzuki and S. H. Lee, Delayed versus accelerated quarkonium formation in a magnetic field, Phys. Rev. C 96, 035203 (2017).
  59. N. Dutta and S. Mazumder, Majorana flipping of quarkonium spin states in transient magnetic field, Eur. Phys. J. C 78, 525 (2018).
  60. J. Hoelck and G. Wolschin, Electromagnetic field effects on ϒ-meson dissociation in PbPb collisions at LHC energies, Eur. Phys. J. A 53, 241 (2017).
  61. P. Bagchi, N. Dutta, B. Chatterjee, and S. P. Adhya, Dissociation of heavy quarkonium states in a rapidly varying strong magnetic field, Mod. Phys. Lett. A 38, 2350035 (2023).
  62. S. Iwasaki, D. Jido, M. Oka, and K. Suzuki, Survival probabilities of charmonia as a clue to measure transient magnetic fields, Phys. Lett. B 820, 136498 (2021).
  63. E. Majorana, Atomi orientati in campo magnetico variabile, Nuovo Cimento 9, 43 (1932).
  64. L. D. Landau, Zur Theorie der energieübertragung bei stössen, Phys. Z. Sowjetunion 1, 88 (1932); edited by D. Ter Haar, 7—A theory of energy transfer on collisions, in Collected Papers of L. D. Landau (Pergamon Press, Oxford, 1965), pp. 52–59.
  65. L. D. Landau, Zur theorie der energieübertragung. II, Phys. Z. Sowjetunion 2, 46 (1932); edited by D. Ter Haar, 9—A theory of energy transfer. II, in Collected Papers of L. D. Landau (Pergamon Press, Oxford, 1965), pp. 63–66.
  66. C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. A 137, 696 (1932).
  67. E. Stückelberg, Theorie der unelastischen stösse zwischen atomen, Helv. Phys. Acta 5, 369 (1932).
  68. O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, Nonadiabatic Landau–Zener–Stückelberg–Majorana transitions, dynamics, and interference, Phys. Rep. 995, 1 (2023).
  69. S. N. Shevchenko, S. Ashhab, and F. Nori, Landau–Zener–Stückelberg interferometry, Phys. Rep. 492, 1 (2010).
  70. E. Eichten, K. Gottfried, T. Kinoshita, J. B. Kogut, K. D. Lane, and T.-M. Yan, Spectrum of charmed quark-antiquark bound states, Phys. Rev. Lett. 34, 369 (1975); 36, 1276(E) (1976).
  71. T. Barnes, S. Godfrey, and E. S. Swanson, Higher charmonia, Phys. Rev. D 72, 054026 (2005).
  72. M. A. Andreichikov, B. O. Kerbikov, V. D. Orlovsky, and Y. A. Simonov, Meson spectrum in strong magnetic fields, Phys. Rev. D 87, 094029 (2013).
  73. M. Kamimura, Nonadiabatic coupled-rearrangement-channel approach to muonic molecules, Phys. Rev. A 38, 621 (1988).
  74. E. Hiyama, Y. Kino, and M. Kamimura, Gaussian expansion method for few-body systems, Prog. Part. Nucl. Phys. 51, 223 (2003).
  75. T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero, Real-time dynamics in U(1) lattice gauge theories with tensor networks, Phys. Rev. X 6, 011023 (2016).
  76. M. Rigobello, S. Notarnicola, G. Magnifico, and S. Montangero, Entanglement generation in (1+1)D QED scattering processes, Phys. Rev. D 104, 114501 (2021).
  77. R. Belyansky, S. Whitsitt, N. Mueller, A. Fahimniya, E. R. Bennewitz, Z. Davoudi, and A. V. Gorshkov, High-energy collision of quarks and mesons in the Schwinger model: From tensor networks to circuit QED, Phys. Rev. Lett. 132, 091903 (2024).
  78. H. Nakamura, Electronic transitions in atomic and molecular dynamic processes, J. Phys. Chem. 88, 4812 (1984).
  79. Y. Kayanuma, Phase coherence and nonadiabatic transition at a level crossing in a periodically driven two-level system, Phys. Rev. B 47, 9940 (1993).

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Phys. Rev. D 113, 054047– Published 26 March, 2026
  • Received 15 January 2026
  • Accepted 24 February 2026
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