- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Stringent Constraints on New Pseudoscalar and Vector Bosons from Precision Hyperfine Splitting Measurements

Cedric Quint1, Fabian Heiße1, Joerg Jaeckel2, Lutz Leimenstoll2, Christoph H. Keitel1, and Zoltán Harman1

PDF

Phys. Rev. Lett. 136, 113001 – Published 19 March, 2026

DOI: https://doi.org/10.1103/rvt1-93v2

Abstract

Axionlike particles and similar new pseudoscalar as well as vector bosons coupled to nucleons and electrons are predicted to lead to spin-dependent forces in atoms and ions. We argue that hyperfine structure measurements in hydrogenlike and lithiumlike charge states are a sensitive probe to this effect. Employing specific differences of these splittings reduces uncertainties due to nuclear effects in hyperfine structure calculations and measurements. Using this, we show that existing measurements on Be provide competitive limits in the region mϕ≳100  keV, confirming, or improving by up to a factor of 2, existing constraints for pseudoscalar couplings, depending on the nuclear model. We also find that future measurements on Cs have a further factor of 2-2.5 improved discovery potential for pseudoscalars and an order of magnitude for new vector bosons when compared with the corresponding current constraints.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (125)

  1. S. G. Karshenboim and V. G. Ivanov, Phys. Lett. B 524, 259 (2002).
  2. J. Jaeckel and S. Roy, Phys. Rev. D 82, 125020 (2010).
  3. S. G. Karshenboim, Phys. Rev. D 82, 113013 (2010).
  4. F. Ficek, D. F. J. Kimball, M. G. Kozlov, N. Leefer, S. Pustelny, and D. Budker, Phys. Rev. A 95, 032505 (2017).
  5. V. Debierre, C. H. Keitel, and Z. Harman, Phys. Lett. B 807, 135527 (2020).
  6. G. Adkins, D. Cassidy, and J. Pérez-Ríos, Phys. Rep. 975, 1 (2022).
  7. T. Sailer, V. Debierre, Z. Harman, F. Heiße, C. König, J. Morgner, B. Tu, A. V. Volotka, C. H. Keitel, K. Blaum, and S. Sturm, Nature (London) 606, 479 (2022).
  8. R. M. Potvliege, New J. Phys. 27, 045002 (2025).
  9. M. Door et al., Phys. Rev. Lett. 134, 063002 (2025).
  10. L. Cong, F. Ficek, P. Fadeev, Y. V. Stadnik, and D. Budker, arXiv:2503.07161.
  11. R. M. Potvliege, A. Nicolson, M. P. A. Jones, and M. Spannowsky, Phys. Rev. A 108, 052825 (2023).
  12. K. Wei, W. Ji, C. Fu, A. Wickenbrock, J. Fang, V. V. Flambaum, and D. Budker, Nat. Commun. 13, 7387 (2022).
  13. W. Ji, W. Li, P. Fadeev, F. Ficek, J. Qin, K. Wei, Y.-C. Liu, and D. Budker, Phys. Rev. Lett. 130, 133202 (2023).
  14. K. A. Beyer, I. A. Valuev, C. H. Keitel, M. Tamburini, and N. S. Oreshkina, Phys. Lett. B 854, 138746 (2024).
  15. A. Wilzewski et al., Phys. Rev. Lett. 134, 233002 (2025).
  16. Z. Xu, X. Heng, G. Tian, D. Gong, L. Cong, W. Ji, D. Budker, and K. Wei, Phys. Rev. Lett. 134, 181801 (2025).
  17. B. Elder, G. Mentasti, E. Pasatembou, C. F. A. Baynham, O. Buchmueller, C. R. Contaldi, C. de Rham, R. Hobson, and A. J. Tolley, Phys. Rev. D 112, 044053 (2025).
  18. J. W. D. Halliday et al., Phys. Rev. Lett. 134, 055001 (2025).
  19. L. Cong et al., Rev. Mod. Phys. 97, 025005 (2025).
  20. J. E. Moody and F. Wilczek, Phys. Rev. D 30, 130 (1984).
  21. B. A. Dobrescu and I. Mocioiu, J. High Energy Phys. 11 (2006) 005.
  22. J. E. Kim, Phys. Rep. 150, 1 (1987).
  23. J. Jaeckel and A. Ringwald, Annu. Rev. Nucl. Part. Sci. 60, 405 (2010).
  24. J. Beacham et al., J. Phys. G 47, 010501 (2020).
  25. P. Agrawal et al., Eur. Phys. J. C 81, 1015 (2021).
  26. R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
  27. S. Weinberg, Phys. Rev. Lett. 40, 223 (1978).
  28. J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
  29. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B166, 493 (1980).
  30. A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980).
  31. M. Dine, W. Fischler, and M. Srednicki, Phys. Lett. 104B, 199 (1981).
  32. L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, Phys. Rep. 870, 1 (2020).
  33. J. P. Conlon, J. High Energy Phys. 05 (2006) 078.
  34. J. P. Conlon, Phys. Rev. Lett. 97, 261802 (2006).
  35. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, Phys. Rev. D 81, 123530 (2010).
  36. M. Cicoli, M. Goodsell, and A. Ringwald, J. High Energy Phys. 10 (2012) 146.
  37. D. J. E. Marsh, Phys. Rep. 643, 1 (2016).
  38. B. S. Acharya and C. Pongkitivanichkul, J. High Energy Phys. 04 (2016) 009.
  39. L. Visinelli and S. Vagnozzi, Phys. Rev. D 99, 063517 (2019).
  40. I. Broeckel, M. Cicoli, A. Maharana, K. Singh, and K. Sinha, J. High Energy Phys. 08 (2021) 059.
  41. M. Demirtas, N. Gendler, C. Long, L. McAllister, and J. Moritz, J. High Energy Phys. 06 (2023) 092.
  42. V. M. Mehta, M. Demirtas, C. Long, D. J. E. Marsh, L. McAllister, and M. J. Stott, J. Cosmol. Astropart. Phys. 07 (2021) 033.
  43. N. Gendler, D. J. E. Marsh, L. McAllister, and J. Moritz, J. Cosmol. Astropart. Phys. 09 (2024) 071.
  44. N. Gendler and D. J. E. Marsh, Phys. Rev. Lett. 134, 081602 (2025).
  45. R. Petrossian-Byrne and G. Villadoro, J. High Energy Phys. 07 (2025) 049.
  46. V. Loladze, A. Platschorre, and M. Reig, J. High Energy Phys. 08 (2025) 182.
  47. J. Jaeckel, Frascati Phys. Ser. 56, 172 (2012).
  48. M. Fabbrichesi, E. Gabrielli, and G. Lanfranchi, The dark photon, SpringerBriefs in Physics (Springer, New York, 2020).
  49. X. G. He, G. C. Joshi, H. Lew, and R. R. Volkas, Phys. Rev. D 43, 22 (1991).
  50. X.-G. He, G. C. Joshi, H. Lew, and R. R. Volkas, Phys. Rev. D 44, 2118 (1991).
  51. J. Heeck and W. Rodejohann, Phys. Rev. D 84, 075007 (2011).
  52. M. Bauer, P. Foldenauer, and J. Jaeckel, J. High Energy Phys. 07 (2018) 094.
  53. L. B. Okun, Sov. Phys. JETP 56, 502 (1982).
  54. B. Holdom, Phys. Lett. 166B, 196 (1986).
  55. R. Foot and X.-G. He, Phys. Lett. B 267, 509 (1991).
  56. B. A. Dobrescu, Phys. Rev. Lett. 94, 151802 (2005).
  57. M. Goodsell, in Proceedings of the 5th Patras Workshop on Axions, WIMPs and WISPs (DESY, Hamburg, Germany, 2009), pp. 165–168.
  58. M. Goodsell, J. Jaeckel, J. Redondo, and A. Ringwald, J. High Energy Phys. 11 (2009) 027.
  59. M. Bullimore, J. P. Conlon, and L. T. Witkowski, J. High Energy Phys. 11 (2010) 142.
  60. M. Cicoli, M. Goodsell, J. Jaeckel, and A. Ringwald, J. High Energy Phys. 07 (2011) 114.
  61. P. G. Camara, L. E. Ibanez, and F. Marchesano, J. High Energy Phys. 09 (2011) 110.
  62. F. Marchesano, D. Regalado, and G. Zoccarato, J. High Energy Phys. 08 (2014) 157.
  63. P. Anastasopoulos, M. Bianchi, D. Consoli, and E. Kiritsis, Fortschr. Phys. 69, 2100034 (2021).
  64. A. Hebecker, J. Jaeckel, and R. Kuespert, J. High Energy Phys. 04 (2024) 116.
  65. E. Sheridan, F. Carta, N. Gendler, M. Jain, D. J. E. Marsh, L. McAllister, N. Righi, K. K. Rogers, and A. Schachner, J. High Energy Phys. 09 (2025) 016.
  66. T. Coudarchet, A. Hebecker, J. Jaeckel, and J. Steiner, arXiv:2510.12874.
  67. J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. 120B, 127 (1983).
  68. L. F. Abbott and P. Sikivie, Phys. Lett. 120B, 133 (1983).
  69. M. Dine and W. Fischler, Phys. Lett. 120B, 137 (1983).
  70. A. E. Nelson and J. Scholtz, Phys. Rev. D 84, 103501 (2011).
  71. P. Arias, D. Cadamuro, M. Goodsell, J. Jaeckel, J. Redondo, and A. Ringwald, J. Cosmol. Astropart. Phys. 06 (2012) 013.
  72. C. B. Adams et al., arXiv:2203.14923.
  73. D. Antypas et al., arXiv:2203.14915.
  74. V. M. Shabaev, A. N. Artemyev, V. A. Yerokhin, O. M. Zherebtsov, and G. Soff, Phys. Rev. Lett. 86, 3959 (2001).
  75. J. Ullmann et al., Nat. Commun. 8, 15484 (2017).
  76. S. Dickopf, B. Sikora, A. Kaiser, M. Müller, S. Ulmer, V. A. Yerokhin, Z. Harman, C. H. Keitel, A. Mooser, and K. Blaum, Nature (London) 632, 757 (2024).
  77. P. Fadeev, Y. V. Stadnik, F. Ficek, M. G. Kozlov, V. V. Flambaum, and D. Budker, Phys. Rev. A 99, 022113 (2019).
  78. M. Moretti, C. H. Keitel, and Z. Harman, Phys. Rev. Lett. 136, 011803 (2026).
  79. V. M. Shabaev, M. B. Shabaeva, and I. I. Tupitsyn, Phys. Rev. A 52, 3686 (1995).
  80. V. M. Shabaev, M. Tomaselli, T. Kühl, A. N. Artemyev, and V. A. Yerokhin, Phys. Rev. A 56, 252 (1997).
  81. A. Schneider, B. Sikora, S. Dickopf, M. Müller, N. S. Oreshkina, A. Rischka, I. A. Valuev, S. Ulmer, J. Walz, Z. Harman, C. H. Keitel, A. Mooser, and K. Blaum, Nature (London) 606, 878 (2022).
  82. V. P. Kosheleva, A. V. Volotka, D. A. Glazov, and S. Fritzsche, Phys. Rev. Res. 2, 013364 (2020).
  83. G. Breit, Phys. Rev. 35, 1447 (1930).
  84. D. E. Zwanziger, Phys. Rev. 121, 1128 (1961).
  85. J. R. Sapirstein, Phys. Rev. Lett. 51, 985 (1983).
  86. T. Schmidt, Z. Phys. 106, 358 (1937).
  87. L. Leimenstoll, Constraining new pseudoscalar bosons using atomic spectroscopy, Bachelor’s thesis, Heidelberg University, 2024.
  88. D. F. J. Kimball, New J. Phys. 17, 073008 (2015).
  89. V. A. Dzuba, V. V. Flambaum, I. B. Samsonov, and Y. V. Stadnik, Phys. Rev. D 98, 035048 (2018).
  90. M. E. Rose and W. H. Furry, Am. J. Phys. 29, 866 (1961).
  91. G. W. F. Drake, Springer Handbook of Atomic, Molecular, and Optical Physics (Springer, New York, 2006).
  92. J. Sapirstein and K. T. Cheng, Phys. Rev. A 63, 032506 (2001).
  93. N. S. Oreshkina, D. A. Glazov, A. V. Volotka, V. M. Shabaev, I. I. Tupitsyn, and G. Plunien, Phys. Lett. A 372, 675 (2008).
  94. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
  95. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
  96. J. Sapirstein and K. T. Cheng, Phys. Rev. A 67, 022512 (2003).
  97. W. R. Johnson, Atomic Structure Theory (Springer, Berlin, Heidelberg, 2007).
  98. A. Bohr and V. F. Weisskopf, Phys. Rev. 77, 94 (1950).
  99. S. Boucard and P. Indelicato, Eur. Phys. J. D 8, 59 (2000).
  100. See Supplemental Material at http://link.aps.org/supplemental/10.1103/rvt1-93v2, for additional derivations, numerical details, and uncertainty estimates, which includes Refs. [101–113].
  101. A. Egl, I. Arapoglou, M. Höcker, K. König, T. Ratajczyk, T. Sailer, B. Tu, A. Weigel, K. Blaum, W. Nörtershäuser, and S. Sturm, Phys. Rev. Lett. 123, 123001 (2019).
  102. V. M. Shabaev, Phys. Rep. 356, 119 (2002).
  103. V. M. Shabaev, M. B. Shabaeva, I. I. Tupitsyn, V. A. Yerokhin, A. N. Artemyev, T. Kühl, M. Tomaselli, and O. M. Zherebtsov, Phys. Rev. A 57, 149 (1998).
  104. J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
  105. M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
  106. O. M. Zherebtsov and V. M. Shabaev, Can. J. Phys. 78, 701 (2000).
  107. A. V. Volotka and G. Plunien, Phys. Rev. Lett. 113, 023002 (2014).
  108. W. Quint, D. L. Moskovkhin, V. M. Shabaev, and M. Vogel, Phys. Rev. A 78, 032517 (2008).
  109. F. Herfurth et al. (for the HITRAP Collaboration), Phys. Scr. 2015, 014065 (2015).
  110. M. Vogel et al., Phys. Scr. 2015, 014066 (2015).
  111. J. Morgner et al., Nature (London) 622, 53 (2023).
  112. D. L. Moskovkin, N. S. Oreshkina, V. M. Shabaev, T. Beier, G. Plunien, W. Quint, and G. Soff, Phys. Rev. A 70, 032105 (2004).
  113. L. V. Skripnikov, S. Schmidt, J. Ullmann, C. Geppert, F. Kraus, B. Kresse, W. Nörtershäuser, A. F. Privalov, B. Scheibe, V. M. Shabaev, M. Vogel, and A. V. Volotka, Phys. Rev. Lett. 120, 093001 (2018).
  114. L. Cong, F. Ficek, P. Fadeev, and D. Budker, Phys. Rev. A 112, 052824 (2025).
  115. S. G. Karshenboim, Phys. Rep. 422, 1 (2005).
  116. V. A. Yerokhin, K. Pachucki, Z. Harman, and C. H. Keitel, Phys. Rev. Lett. 107, 043004 (2011).
  117. V. A. Yerokhin, K. Pachucki, Z. Harman, and C. H. Keitel, Phys. Rev. A 85, 022512 (2012).
  118. I. Kuzmenko, T. Kuzmenko, Y. Avishai, and Y. B. Band, Phys. Rev. A 108, 052804 (2023).
  119. C. Delaunay, C. Frugiuele, E. Fuchs, and Y. Soreq, Phys. Rev. D 96, 115002 (2017).
  120. H. M. Chang, H. T. Wong, M. H. Chou, M. Deniz, H. X. Huang, F. S. Lee, H. B. Li, J. Li, H. Y. Liao, S. T. Lin, V. Singh, S. C. Wu, and B. Xin, Phys. Rev. D 75, 052004 (2007).
  121. D. Basilico et al. (BOREXINO Collaboration), Eur. Phys. J. C 85, 1182 (2025).
  122. P. Carenza and G. Lucente, Phys. Rev. D 103, 123024 (2021).
  123. A. Lella, P. Carenza, G. Co’, G. Lucente, M. Giannotti, A. Mirizzi, and T. Rauscher, Phys. Rev. D 109, 023001 (2024).
  124. W. R. Johnson and G. Soff, At. Data Nucl. Data Tables 33, 405 (1985).

  125. The distance between the magnetic field source and the ion is large compared with the range of the NP potential, 1/mϕ/Z, relevant for our constraints. Thus, we can neglect the effect that new bosons may have on this potential.

Outline

Information

Phys. Rev. Lett. 136, 113001– Published 19 March, 2026
  • Received 12 June 2025
  • Revised 28 October 2025
  • Accepted 20 February 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