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

Demonstration of Deuterium’s Enhanced Sensitivity to Symmetry Violations Governed by the Standard-Model Extension

A. Nanda1,2, D. Comparat3, O. Dulieu3, S. Lahs3,*, C. Malbrunot4,5,6, L. Nowak1,2, M. C. Simon1,†,‡, and E. Widmann1,‡

  • *Present address: Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien 1020, Vienna, Austria.
  • †Contact author: martin.simon@oeaw.ac.at
  • ‡Present address: Marietta Blau Institute for Particle Physics, Dominikanerbastei 16, 1010 Vienna, Austria.

Phys. Rev. Lett. 137, 031802 – Published 14 July, 2026

DOI: https://doi.org/10.1103/dqvd-15q4

Abstract

We have performed hyperfine spectroscopy of two transitions in ground-state deuterium and searched for violations of CPT and Lorentz symmetry that would manifest as sidereal variations of the observed transition frequencies. Several nonrelativistic proton coefficients of the Standard-Model extension framework have been addressed. The spin-independent coefficients with momentum power k=2, 4 are constrained for the first time. Bounds on spin-dependent coefficients are improved by exploiting a sensitivity enhancement originating from the relative momenta of the nucleons in the deuteron. The best previous constraints by hydrogen maser measurements are surpassed by 4 and 14 orders of magnitude for coefficients with k=2 and 4, respectively.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (67)

  1. K. Pachucki, M. Weitz, and T. W. Hänsch, Theory of the hydrogen-deuterium isotope shift, Phys. Rev. A 49, 2255 (1994).
  2. S. Rau, F. Heiße, F. Köhler-Langes, S. Sasidharan, R. Haas, D. Renisch, C. E. Düllmann, W. Quint, S. Sturm, and K. Blaum, Penning trap mass measurements of the deuteron and the HD+ molecular ion, Nature (London) 585, 43 (2020).
  3. V. Mossa, K. Stöckel, F. Cavanna, F. Ferraro, M. Aliotta, F. Barile, D. Bemmerer, A. Best, A. Boeltzig, C. Broggini et al., The baryon density of the universe from an improved rate of deuterium Burning, Nature (London) 587, 210 (2020).
  4. J. E. Nafe and E. B. Nelson, The hyperfine structure of hydrogen and deuterium, Phys. Rev. 73, 718 (1948).
  5. R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, L. M. P. Fernandes et al., The size of the proton, Nature (London) 466, 213 (2010).
  6. A. Antognini, F. Nez, K. Schuhmann, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, M. Diepold et al., Proton structure from the measurement of 2S-2P transition frequencies of muonic hydrogen, Science 339, 417 (2013).
  7. R. Pohl, F. Nez, L. M. P. Fernandes, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, M. Diepold et al., Laser spectroscopy of muonic Deuterium, Science 353, 669 (2016).
  8. H. Gao and M. Vanderhaeghen, The proton charge radius, Rev. Mod. Phys. 94, 015002 (2022).
  9. O. Hernandez, A. Ekström, N. Nevo Dinur, C. Ji, S. Bacca, and N. Barnea, The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties, Phys. Lett. B 778, 377 (2018).
  10. D. Gotta, Precision spectroscopy of light exotic atoms, Prog. Part. Nucl. Phys. 52, 133 (2004).
  11. T. Strauch, F. D. Amaro, D. F. Anagnostopoulos, P. Bühler, D. S. Covita, H. Gorke, D. Gotta, A. Gruber, A. Hirtl, P. Indelicato et al., Precision determination of the dπ ↔ nn transition strength at threshold, Phys. Rev. Lett. 104, 142503 (2010).
  12. M. Iwasaki, R. S. Hayano, T. M. Ito, S. N. Nakamura, T. P. Terada, D. R. Gill, L. Lee, A. Olin, M. Salomon, S. Yen et al., Observation of kaonic hydrogen Kα x rays, Phys. Rev. Lett. 78, 3067 (1997).
  13. G. Beer, A. M. Bragadireanu, M. Cargnelli, C. Curceanu-Petrascu, J.-P. Egger, H. Fuhrmann, C. Guaraldo, M. Iliescu, T. Ishiwatari, K. Itahashi et al., Measurement of the kaonic hydrogen x-ray spectrum, Phys. Rev. Lett. 94, 212302 (2005).
  14. C. Curceanu, C. Guaraldo, M. Iliescu, M. Cargnelli, R. Hayano, J. Marton, J. Zmeskal, T. Ishiwatari, M. Iwasaki, S. Okada et al., The modern era of light kaonic Atom experiments, Rev. Mod. Phys. 91, 025006 (2019).
  15. J. Richard and M. Sainio, Nuclear effects in protonium, Phys. Lett. B 110, 349 (1982).
  16. S. Wycech, A. Green, and J. Niskanen, On the energy levels in antiprotonic deuterium, Phys. Lett. B 152, 308 (1985).
  17. C. Baker, C. Batty, S. Clark, J. Moir, S. Sakamoto, J. Davies, J. Lowe, J. Nelson, G. Pyle, A. Selvarajah et al., Measurement of x-rays from anti-protonic hydrogen and deuterium, Nucl. Phys. A483, 631 (1988).
  18. M. Augsburger, D. Anagnostopoulos, G. Borchert, D. Chatellard, J.-P. Egger, P. El-Khoury, H. Gorke, D. Gotta, P. Hauser, P. Indelicato et al., Measurement of the strong interaction parameters in antiprotonic deuterium, Phys. Lett. B 461, 417 (1999).
  19. M. Augsburger, D. Anagnostopoulos, G. Borchert, D. Chatellard, J.-P. Egger, P. El-Khoury, H. Gorke, D. Gotta, P. Hauser, P. Indelicato et al., Measurement of the strong interaction parameters in antiprotonic hydrogen and probable evidence for an interference with inner bremsstrahlung, Nucl. Phys. A658, 149 (1999).
  20. D. F. Phillips, M. A. Humphrey, E. M. Mattison, R. E. Stoner, R. F. C. Vessot, and R. L. Walsworth, Limit on Lorentz and CPT Violation of the proton using a hydrogen maser, Phys. Rev. D 63, 111101 (2001).
  21. M. A. Humphrey, D. F. Phillips, E. M. Mattison, R. F. C. Vessot, R. E. Stoner, and R. L. Walsworth, Testing CPT and Lorentz symmetry with hydrogen masers, Phys. Rev. A 68, 063807 (2003).
  22. R. M. Potvliege, A. Nicolson, M. P. A. Jones, and M. Spannowsky, Deuterium spectroscopy for enhanced bounds on physics beyond the standard model, Phys. Rev. A 108, 052825 (2023).
  23. V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with hydrogen, antihydrogen, and related systems, Phys. Rev. D 92, 056002 (2015).
  24. A. J. Vargas, Prospects for testing CPT and Lorentz symmetry with deuterium ground-state Zeeman-hyperfine transitions, Phys. Rev. D 109, 055001 (2024).
  25. I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, A new method of measuring nuclear magnetic moment, Phys. Rev. 53, 318 (1938).
  26. D. Colladay and V. A. Kostelecký, CPT violation and the standard model, Phys. Rev. D 55, 6760 (1997).
  27. D. Colladay and V. A. Kostelecký, Lorentz-violating extension of the standard model, Phys. Rev. D 58, 116002 (1998).
  28. R. Bluhm, V. A. Kostelecký, and N. Russell, CPT and Lorentz tests in hydrogen and antihydrogen, Phys. Rev. Lett. 82, 2254 (1999).
  29. G. Breit and I. I. Rabi, Measurement of nuclear spin, Phys. Rev. 38, 2082 (1931).
  30. D. J. Wineland and N. F. Ramsey, Atomic Deuterium maser, Phys. Rev. A 5, 821 (1972).
  31. P. J. Mohr, D. B. Newell, B. N. Taylor, and E. Tiesinga, Codata recommended values of the fundamental physical constants: 2022, Rev. Mod. Phys. 97, 025002 (2025).
  32. V. A. Kostelecký and N. Russell, Data tables for Lorentz and CPT violation, Rev. Mod. Phys. 83, 11 (2011).
  33. V. A. Kostelecký and M. Mewes, Electrodynamics with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 80, 015020 (2009).
  34. V. A. Kostelecký and M. Mewes, Fermions with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 88, 096006 (2013).
  35. V. A. Kostelecký and Z. Li, Gauge field theories with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 99, 056016 (2019).
  36. V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with clock-comparison experiments, Phys. Rev. D 98, 036003 (2018).
  37. E. Widmann, R. Hayano, M. Hori, and T. Yamazaki, Measurement of the hyperfine structure of antihydrogen, Nucl. Instrum. Methods Phys. Res., Sect. B 214, 31 (2004).
  38. M. Diermaier, C. Jepsen, B. Kolbinger, C. Malbrunot, O. Massiczek, C. Sauerzopf, M. Simon, J. Zmeskal, and E. Widmann, In-beam measurement of the hydrogen hyperfine splitting and prospects for antihydrogen spectroscopy, Nat. Commun. 8, 1 (2017).
  39. C. Malbrunot, M. Diermaier, M. Simon, C. Amsler, S. Arguedas Cuendis, H. Breuker, C. Evans, M. Fleck, B. Kolbinger, A. Lanz et al., A hydrogen beam to characterize the ASACUSA antihydrogen hyperfine spectrometer, Nucl. Instrum. Methods Phys. Res., Sect. A 935, 110 (2019).
  40. L. Nowak, C. Malbrunot, M. Simon, C. Amsler, S. Arguedas Cuendis, S. Lahs, A. Lanz, A. Nanda, M. Wiesinger, T. Wolz et al., CPT and Lorentz symmetry tests with hydrogen using a novel in-beam hyperfine spectroscopy method applicable to antihydrogen experiments, Phys. Lett. B 858, 139012 (2024).
  41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/dqvd-15q4 for details on beam path Sec. A.1, which includes Ref. [42], details on oscillating magnetic field Sec. A.2, which includes Refs. [43–45], details on static magnetic field Sec. A.3, which includes Ref. [45], details on data acquisition protocol Sec. B, and for an example and a comprehensive table on SME constraints Sec. C, which includes Refs. [20,23,24].
  42. https://e-opthos.com/microwave-cavities.
  43. M. W. Reynolds, M. E. Hayden, and W. N. Hardy, Hyperfine resonance of atomic deuterium at 1 K, J. Low Temp. Phys. 84, 87 (1991).
  44. https://cubicure.com/en/hot-lithography/.
  45. COMSOL Multiphysics, https://www.comsol.com.
  46. G. Özşahin, T. Şimşek, M. Ünlü, O. Kiriş, S. Köse, H. Mustaçoğlu, F. Öztürk, and V. Akan, Parametric analysis of double-split ring resonator as a reflectarray unit cell, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 101–102.
  47. C. Debus and P. H. Bolivar, Frequency selective surfaces for high sensitivity terahertz sensing, Appl. Phys. Lett. 91, 184102 (2007).
  48. N. Kaur, F. Frank, J. Pinto, P. Tuckey, and P.-E. Pottie, A 500-km cascaded white rabbit link for high-performance frequency dissemination, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 69, 892 (2022).
  49. E. Cantin, M. Tønnes, R. L. Targat, A. Amy-Klein, O. Lopez, and P.-E. Pottie, An accurate and robust metrological network for coherent optical frequency Dissemination, New J. Phys. 23, 053027 (2021).
  50. https://www.refimeve.fr/index.php/en/.
  51. The theoretical analysis toward the present experiment [24] assumes ϑ≃49° corresponding to the opposite magnetic field direction than applied in this work.

  52. C. Killian, Z. Burkley, P. Blumer, P. Crivelli, F. P. Gustafsson, O. Hanski, A. Nanda, F. Nez, V. Nesvizhevsky, S. Reynaud et al., GRASIAN: towards the first Demonstration of gravitational quantum states of atoms with a cryogenic hydrogen beam, Eur. Phys. J. D 77, 50 (2023).
  53. C. Killian, P. Blumer, P. Crivelli, O. Hanski, D. Kloppenburg, F. Nez, V. Nesvizhevsky, S. Reynaud, K. Schreiner, M. Simon et al., GRASIAN: shaping and characterization of the cold hydrogen and deuterium beams for the forthcoming first demonstration of gravitational quantum states of atoms, Eur. Phys. J. D 78, 132 (2024).
  54. N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78, 695 (1950).
  55. N. F. Ramsey, Experiments with separated oscillatory fields and hydrogen masers, Rev. Mod. Phys. 62, 541 (1990).
  56. A. Nanda, Progress towards ramsey hyperfine spectroscopy in asacusa, in CPT and Lorentz Symmetry (World Scientific, Singapore, 2020), pp. 201–203.
  57. T. Schmidt, Über die magnetischen Momente der Atomkerne, Z. Phys. 106, 358 (1937).
  58. J. T. VanderPlas, Understanding the Lomb–Scargle periodogram, Astrophys. J. Suppl. Ser. 236, 16 (2018).
  59. J. T. VanderPlas and Željko Ivezić,Periodograms for multiband astronomical time series, Astrophys. J. 812, 18 (2015).
  60. J. Vanderplas, A. J. Connolly, Željko Ivezić, and A. G. Gray, Introduction to astroML: Machine learning for astrophysics, in 2012 Conference on Intelligent Data Understanding, vol. 47 (2012).
  61. N. R. Lomb, Least-squares frequency analysis of unequally spaced data, Astrophys. Space Sci. 39, 447 (1976).
  62. J. D. Scargle,Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data, Astrophys. J. 263, 835 (1982).
  63. A. M. Price-Whelan, P. L. Lim, N. Earl, N. Starkman, L. Bradley, D. L. Shupe, A. A. Patil, L. Corrales, C. E. Brasseur et al. (Astropy Collaboration), The Astropy project: Sustaining and growing a community-oriented open-source project and the latest major release (v5.0) of the core package, Astrophys. J. 935, 167 (2022).
  64. A. M. Price-Whelan, B. M. Sipőcz, H. M. Günther, P. L. Lim, S. M. Crawford, S. Conseil, D. L. Shupe, M. W. Craig, N. Dencheva et al. (Astropy Collaboration), The Astropy project: Building an open-science project and status of the v2.0 core package, Astron. J. 156, 123 (2018).
  65. T. P. Robitaille, E. J. Tollerud, P. Greenfield, M. Droettboom, E. Bray, T. Aldcroft, M. Davis, A. Ginsburg, A. M. Price-Whelan et al. (Astropy Collaboration), Astropy: A community python package for astronomy, Astron. Astrophys. 558, A33 (2013).
  66. L. S. Dreissen, C.-H. Yeh, H. A. Fürst, K. C. Grensemann, and T. E. Mehlstäubler, Improved bounds on Lorentz violation from composite pulse Ramsey spectroscopy in a trapped ion, Nat. Commun. 13, 7314 (2022).
  67. R. V. Baluev, Assessing the statistical significance of periodogram peaks, Mon. Not. R. Astron. Soc. 385, 1279 (2008).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation