- 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

Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions. II. Hyperfine-Zeeman spectrum

Graham M. Shore*

  • Department of Physics, Faculty of Science and Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom

  • *Contact author: g.m.shore@swansea.ac.uk
PDF

Phys. Rev. D 112, 056016 – Published 15 September, 2025

DOI: https://doi.org/10.1103/vby7-p924

Abstract

Fundamental principles of quantum field theory (QFT) such as Lorentz invariance, CPT symmetry, and locality may be tested to extremely high precision in atomic and molecular spectroscopy. The narrow natural linewidth of rovibrational states in the hydrogen molecular ion H2+ and its antimatter counterpart H¯2− make these ideal candidates, and give O(mp/me) increased sensitivity to Lorentz and CPT violation in the proton sector compared to H and H¯ atoms. In a previous paper, we presented a detailed analysis of the rovibrational spectrum of H2+ and H¯2− in an effective QFT encoding Lorentz and CPT violation, focusing on spin-independent effects. Here, we extend this analysis to include the full hyperfine-Zeeman spectrum and include spin-dependent Lorentz and CPT violating operators in the effective theory. The results demonstrate how constraints on these symmetry-violating couplings may be extracted from specific rovibrational transitions between hyperfine-Zeeman states in the presence of an applied magnetic field.

View figure in article

Physics Subject Headings (PhySH)

See Also

Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions. I. Rovibrational states

Graham M. Shore
Phys. Rev. D 112, 056015 (2025)

Article Text

References (25)

  1. S. Schiller, Precision spectroscopy of molecular hydrogen ions: An introduction, Contemp. Phys. 63, 247 (2022) and supplementary material.
  2. M. R. Schenkel, S. Alighanbari, and S. Schiller, Laser spectroscopy of a rovibrational transition in the molecular hydrogen ion H2+, Nat. Phys. 20, 383 (2024).
  3. S. Schiller and J.-P. Karr, Prospects for the determination of fundamental constants with beyond-state-of-the-art uncertainty using molecular hydrogen ion spectroscopy, Phys. Rev. A 109, 042825 (2024).
  4. M. Ahmadi et al. (ALPHA Collaboration), Observation of the 1S−2S transition in trapped antihydrogen, Nature (London) 541, 506 (2016).
  5. M. Ahmadi et al. (ALPHA Collaboration), Characterization of the 1S−2S transition in antihydrogen, Nature (London) 557, 71 (2018).
  6. E. G. Myers, CPT tests with the antihydrogen molecular ion, Phys. Rev. A 98, 010101(R) (2018).
  7. M. C. Zammit et al., Laser-driven production of the antihydrogen molecular ion, Phys. Rev. A 100, 042709 (2019).
  8. M. C. Zammit, C. J. Baker, S. Jonsell, S. Eriksson, and M. Charlton, Antihydrogen chemistry, Phys. Rev. A 111, 050101 (2025).
  9. G. M. Shore, preceding paper, Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions. I. Rovibrational states, Phys. Rev. D 112, 056015 (2025).
  10. H. Muller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, Tests of Lorentz invariance using hydrogen molecules, Phys. Rev. D 70, 076004 (2004).
  11. V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with hydrogen, antihydrogen, and related systems, Phys. Rev. D 92, 056002 (2015).
  12. M. Charlton, S. Eriksson, and G. M. Shore, Antihydrogen and Fundamental Physics (Springer, New York, 2020); arXiv:2002.09348.
  13. C. J. Baker et al., Precision spectroscopy of the hyperfine components of the 1S–2S transition in antihydrogen, Nat. Phys. 21, 201 (2025).
  14. D. Colladay and V. A. Kostelecky, Lorentz violating extension of the standard model, Phys. Rev. D 58, 116002 (1998).
  15. A. Kostelecký and M. Mewes, Fermions with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 88, 096006 (2013).
  16. V. A. Kostelecky and C. D. Lane, Nonrelativistic quantum Hamiltonian for Lorentz violation, J. Math. Phys. (N.Y.) 40, 6245 (1999).
  17. T. J. Yoder and G. S. Adkins, Higher order corrections to the hydrogen spectrum from the Standard-Model extension, Phys. Rev. D 86, 116005 (2012).
  18. V. A. Kostelecky and N. Russell, Data tables for Lorentz and CPT violation, Rev. Mod. Phys. 83, 11 (2011).
  19. A. J. Vargas, Prospects for testing Lorentz and CPT symmetry with H2+ and H¯2−, arXiv:2503.06306.
  20. V. I. Korobov, L. Hilico, and J.-P. Karr, Hyperfine structure in the hydrogen molecular ion, Phys. Rev. A 74, 040502(R) (2006).
  21. J-P. KarrF. Bielsa, A. Douillet, J. P. Gutierrez, V. I. Korobov, and L. Hilico, Vibrational spectroscopy of H2+: Hyperfine structure of two-photon transitions, Phys. Rev. A 77, 06430 (2008).
  22. J.-P. Karr, V. I. Korobov, and L. Hilico, Vibrational spectroscopy of H2+: Precise evaluation of the Zeeman effect, Phys. Rev. A 77, 062507 (2008).
  23. M. Ahmadi et al. (ALPHA Collaboration), Observation of the 1S–2P Lyman-α transition in antihydrogen, Nature (London) 561, 211 (2018).
  24. S. Schiller and V. I. Korobov, Cancelling spin-dependent contributions and systematic shifts in precision spectroscopy of molecular hydrogen ions, Phys. Rev. A 98, 022511 (2018).
  25. K. B. Jefferts, Hyperfine structure in the molecular ion H2+, Phys. Rev. Lett. 23, 1476 (1969).

Outline

Information

Phys. Rev. D 112, 056016– Published 15 September, 2025
  • Received 22 May 2025
  • Accepted 22 July 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