- 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. III. Rovibrational spectrum and the nonminimal standard model extension

Graham M. Shore*

  • Centre for Quantum Fields and Gravity, Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom

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

Phys. Rev. D 114, 065006 – Published 8 September, 2026

DOI: https://doi.org/10.1103/p2bd-m44y

Abstract

Rovibrational transitions in the hydrogen and antihydrogen molecular ions H2+ and H¯2− offer the possibility of testing Lorentz and CPT symmetry to extremely high precision, in principle attaining O(10−17). In this paper, the third in a series, we give a comprehensive derivation of the rovibrational spectrum of H2+ and H¯2− in the standard model extension (SME), an effective quantum field theory incorporating Lorentz and CPT violation. New developments described here include a complete analysis of the molecular dynamics from first principles in terms of the spherical tensor representation of the SME couplings, the systematic extension of our previous results to the nonminimal SME, a full description of the quantum number dependence of the rovibrational energy levels in the spherical tensor formalism with both high and low background magnetic fields, and an extended discussion of sidereal and annual variations of transition frequencies arising from both rotations and Lorentz boosts. The resulting sensitivity of the rovibrational spectrum to an extended range of SME couplings, together with the ability to isolate their individual effects using the quantum number dependence of the transition frequencies, enhances the opportunities to detect Lorentz and CPT symmetry breaking through rovibrational spectroscopy of H2+ and H¯2−.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (26)

  1. M. Charlton, S. Eriksson, and G. M. Shore, Antihydrogen and Fundamental Physics (Springer, New York, 2020), 10.1007/978-3-030-51713-7.
  2. S. Schiller, Precision spectroscopy of molecular hydrogen ions: An introduction, Contemp. Phys. 63, 247 (2022) and Supplementary material.
  3. G. M. Shore, Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions. I. Rovibrational states, Phys. Rev. D 112, 056015 (2025).
  4. G. M. Shore, Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions. II. Hyperfine-Zeeman spectrum, Phys. Rev. D 112, 056016 (2025).
  5. D. Colladay and V. A. Kostelecky, Lorentz violating extension of the standard model, Phys. Rev. D 58, 116002 (1998).
  6. A. Kostelecký and M. Mewes, Fermions with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 88, 096006 (2013).
  7. 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).
  8. M. C. Zammit et al., Laser-driven production of the antihydrogen molecular ion, Phys. Rev. A 100, 042709 (2019).
  9. E. G. Myers, CPT tests with the antihydrogen molecular ion, Phys. Rev. A 98, 010101(R) (2018).
  10. M. C. Zammit, C. J. Baker, S. Jonsell, S. Eriksson, and M. Charlton, Antihydrogen chemistry, Phys. Rev. A 111, 050101 (2025).
  11. M. Ahmadi et al. (ALPHA Collaboration), Characterization of the 1S-2S transition in antihydrogen, Nature (London) 557, 71 (2018).
  12. C. J. Baker et al., Precision spectroscopy of the hyperfine components of the 1S–2S transition in antihydrogen, Nat. Phys. 21, 201 (2025).
  13. V. A. Kostelecky and N. Russell, Data tables for Lorentz and CPT violation, Rev. Mod. Phys. 83, 11 (2011).
  14. S. Schiller et al., Towards a future test of CPT invariance by spectroscopy of H2+ and anti-H2+, in Talk at Workshop All that Antimatters in the Universe (CERN, Geneva, 2026).
  15. A. J. Vargas, Prospects for testing Lorentz and CPT symmetry with H2+ and H¯2−, arXiv:2503.06306.
  16. A. J. Vargas, Nonminimal Lorentz violation in atomic and molecular spectroscopy experiments, arXiv:2603.08298.
  17. V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with hydrogen, antihydrogen, and related systems, Phys. Rev. D 92, 056002 (2015).
  18. H. Muller, S. Herrmann, A. Saenz, A. Peters, and C. Lammerzahl, Tests of Lorentz invariance using hydrogen molecules, Phys. Rev. D 70, 076004 (2004).
  19. V. A. Kostelecky and C. D. Lane, Nonrelativistic quantum Hamiltonian for Lorentz violation, J. Math. Phys. (N.Y.) 40, 6245 (1999).
  20. A. Carrington, I. R. McNab, and C. A. Montgomerie, Spectroscopy of the hydrogen molecular ion, J. Phys. B 22, 3551 (1989).
  21. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
  22. 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).
  23. 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).
  24. V. I. Korobov, L. Hilico, and J.-Ph. Karr, Hyperfine structure in the hydrogen molecular ion, Phys. Rev. A 74, 040502(R) (2006).
  25. J-P. Karr et al., Vibrational spectroscopy of H2+: Hyperfine structure of two-photon transitions, Phys. Rev. A 77, 06430 (2008).
  26. J.-Ph. Karr, V. I. Korobov, and L. Hilico, Vibrational spectroscopy of H2+: Precise evaluation of the Zeeman effect, Phys. Rev. A 77, 062507 (2008).

Outline

Information

Phys. Rev. D 114, 065006– Published 8 September, 2026
  • Received 24 April 2026
  • Accepted 11 August 2026
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