- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

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

Relative enhancement of low-mass vector-boson exchange in states with higher angular momentum: Parity nonconservation in hydrogen

V. A. Dzuba*, V. V. Flambaum†, and G. K. Vong‡

  • *Contact author: v.dzuba@unsw.edu.au
  • †Contact author: v.flambaum@unsw.edu.au
  • ‡Contact author: g.vong@unsw.edu.au
PDF

APS Open Sci. 1, 000170 – Published 13 October, 2026

DOI: https://doi.org/10.1103/zqzd-t38c

Abstract

Models of unification predict additional Z′ boson, which contributes to parity nonconservation (PNC) in atoms. If Z′ boson is light, ratio of Z′-boson contribution to the standard model Z-boson contribution to atomic PNC increases with decreasing nuclear charge Z faster than 1/Z2. This motivated our previous study of PNC in hydrogen and deuterium, where s−p wave mixing induced by the weak interaction was considered. An even more pronounced relative enhancement occurs when higher-angular-momentum states are involved, such as in the p−d weak matrix elements. A light boson mediates a long-range interaction, in contrast to the effectively contactlike interaction mediated by the standard model Z boson. Consequently, higher-angular-momentum states provide a background-free system: Their suppressed overlap with the nucleus strongly reduces the standard model contribution while leaving the long-range Z′ contribution unsuppressed.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (28)

  1. V. A. Dzuba and V. V. Flambaum, Parity violation and electric dipole moments in atoms and molecules, Int. J. Mod. Phys. E 21, 1230010 (2012).
  2. B. M. Roberts, V. A. Dzuba, and V. V. Flambaum, Parity and time-reversal violation in atomic systems, Annu. Rev. Nucl. Part. Sci. 65, 63 (2015).
  3. C. Bouchiat and P. Fayet, Constraints on the parity-violating couplings of a new gauge boson, Phys. Lett. B 608, 87 (2005).
  4. R. Diener, S. Godfrey, and I. Turan, Constraining extra neutral gauge bosons with atomic parity violation measurements, Phys. Rev. D 86, 115017 (2012).
  5. V. A. Dzuba, V. V. Flambaum, and Y. V. Stadnik, Probing low-mass vector bosons with parity nonconservation and nuclear anapole moment measurements in atoms and molecules, Phys. Rev. Lett. 119, 223201 (2017).
  6. D. Antypas, A. Fabricant, J. E. Stalnaker, K. Tsigutkin, V. V. Flambaum, and D. Budker, Isotopic variation of parity violation in atomic ytterbium, Nat. Phys. 15, 120 (2019).
  7. C. S. Wood, S. C. Bennett, D. Cho, B. P. Masterson, J. L. Roberts, C. E. Tanner, and C. E. Wieman, Measurement of parity nonconservation and an anapole moment in cesium, Science 275, 1759 (1997).
  8. A. T. Nguyen, D. Budker, D. DeMille, and M. Zolotorev, Search for parity nonconservation in atomic dysprosium, Phys. Rev. A 56, 3453 (1997).
  9. Y. B. Zel'dovich, Parity nonconservation in the first order in the weak-interaction constant in electron scattering and other effects, Sov. Phys. JETP 9, 682 (1959).
  10. F. C. Michel, Neutral weak interaction currents, Phys. Rev. 138, B408 (1965).
  11. R. N. Cahn and G. L. Kane, Parity violations in hydrogen and the fundamental structure of the weak current, Phys. Lett. B 71, 348 (1977).
  12. R. W. Dunford and R. J. Holt, Parity violation in hydrogen revisited, J. Phys. G: Nucl. Part. Phys. 34, 2099 (2007).
  13. R. W. Dunford and R. J. Holt, Parity nonconservation in hydrogen, Hyperfine Interact. 200, 45 (2011).
  14. C. Rasor and D. C. Yost, Laser-based measurement of parity violation in hydrogen, Phys. Rev. A 102, 032801 (2020).
  15. J. Li, A. Derevianko, and D. S. Elliott, Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the 2s–3s or 2s–4s transition in hydrogen, Phys. Rev. A 109, 012808 (2024).
  16. J. Erler, A. Kurylov, and M. J. Ramsey-Musolf, Weak charge of the proton and new physics, Phys. Rev. D 68, 016006 (2003).
  17. D. Androić et al. (Jefferson Lab Qweak Collaboration), Precision measurement of the weak charge of the proton, Nature (London) 557, 207 (2018).
  18. R. D. Carlini, W. T. H. van Oers, M. L. Pitt, and G. R. Smith, Determination of the proton's weak charge and its constraints on the standard model, Annu. Rev. Nucl. Part. Sci. 69, 191 (2019).
  19. P. S. B. Dev, W. Rodejohann, X.-J. Xu, and Y. Zhang, Searching for Z′ bosons at the P2 experiment, J. High Energy Phys. 06 (2021) 039.
  20. A. W. Thomas, X. G. Wang, and A. G. Williams, Sensitivity of parity-violating electron scattering to a dark photon, Phys. Rev. Lett. 129, 011807 (2022).
  21. A. W. Thomas, X. G. Wang, and A. G. Williams, Dark photon in parity-violating electron scatterings, arXiv:2505.07279.
  22. V. A. Dzuba, V. V. Flambaum, and G. K. Vong, Parity nonconservation in Rb and Sr+ due to a low-mass vector boson, Phys. Rev. A 113, 052808 (2026).
  23. V. A. Dzuba, V. V. Flambaum, and G. K. Vong, Parity nonconservation in hydrogen induced by low-mass vector-boson exchange, Phys. Rev. A 113, 062817 (2026).
  24. M. Tanabashi et al., Review of particle physics, Phys. Rev. D 98, 030001 (2018).
  25. V. V. Flambaum and I. B. Samsonov, Effects of dispersion parity-violating interaction in electron scattering and atoms, Phys. Rev. D 114, L011302 (2026).
  26. Energy and width of 3dj state appear explicitly if we multiply this amplitude by a factor describing decay of 3dj state to a final state f, 〈f|Dq|3dj〉/(E−E3dj+iΓ3dj/2).
  27. V. V. Flambaum and I. B. Khriplovich, P-odd nuclear forces—A source of parity violation in atoms, Sov. Phys. JETP 52, 835 (1980).
  28. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin, 1957).

Outline

Information

APS Open Sci. 1, 000170– Published 13 October, 2026
Vol. 1
  • Received 19 July 2026
  • Accepted 5 October 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation