- Open Access
Demonstration of Deuterium’s Enhanced Sensitivity to Symmetry Violations Governed by the Standard-Model Extension
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 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 , 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 and 4, respectively.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (67)
- K. Pachucki, M. Weitz, and T. W. Hänsch, Theory of the hydrogen-deuterium isotope shift, Phys. Rev. A 49, 2255 (1994).
- 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).
- 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).
- J. E. Nafe and E. B. Nelson, The hyperfine structure of hydrogen and deuterium, Phys. Rev. 73, 718 (1948).
- 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).
- 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).
- 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).
- H. Gao and M. Vanderhaeghen, The proton charge radius, Rev. Mod. Phys. 94, 015002 (2022).
- 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).
- D. Gotta, Precision spectroscopy of light exotic atoms, Prog. Part. Nucl. Phys. 52, 133 (2004).
- 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 transition strength at threshold, Phys. Rev. Lett. 104, 142503 (2010).
- 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 x rays, Phys. Rev. Lett. 78, 3067 (1997).
- 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).
- 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).
- J. Richard and M. Sainio, Nuclear effects in protonium, Phys. Lett. B 110, 349 (1982).
- S. Wycech, A. Green, and J. Niskanen, On the energy levels in antiprotonic deuterium, Phys. Lett. B 152, 308 (1985).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with hydrogen, antihydrogen, and related systems, Phys. Rev. D 92, 056002 (2015).
- A. J. Vargas, Prospects for testing CPT and Lorentz symmetry with deuterium ground-state Zeeman-hyperfine transitions, Phys. Rev. D 109, 055001 (2024).
- I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, A new method of measuring nuclear magnetic moment, Phys. Rev. 53, 318 (1938).
- D. Colladay and V. A. Kostelecký, CPT violation and the standard model, Phys. Rev. D 55, 6760 (1997).
- D. Colladay and V. A. Kostelecký, Lorentz-violating extension of the standard model, Phys. Rev. D 58, 116002 (1998).
- R. Bluhm, V. A. Kostelecký, and N. Russell, CPT and Lorentz tests in hydrogen and antihydrogen, Phys. Rev. Lett. 82, 2254 (1999).
- G. Breit and I. I. Rabi, Measurement of nuclear spin, Phys. Rev. 38, 2082 (1931).
- D. J. Wineland and N. F. Ramsey, Atomic Deuterium maser, Phys. Rev. A 5, 821 (1972).
- 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).
- V. A. Kostelecký and N. Russell, Data tables for Lorentz and CPT violation, Rev. Mod. Phys. 83, 11 (2011).
- V. A. Kostelecký and M. Mewes, Electrodynamics with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 80, 015020 (2009).
- V. A. Kostelecký and M. Mewes, Fermions with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 88, 096006 (2013).
- V. A. Kostelecký and Z. Li, Gauge field theories with Lorentz-violating operators of arbitrary dimension, Phys. Rev. D 99, 056016 (2019).
- V. A. Kostelecký and A. J. Vargas, Lorentz and CPT tests with clock-comparison experiments, Phys. Rev. D 98, 036003 (2018).
- 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).
- 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).
- 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).
- 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).
- 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].
- https://e-opthos.com/microwave-cavities.
- 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).
- https://cubicure.com/en/hot-lithography/.
- COMSOL Multiphysics, https://www.comsol.com.
- 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.
- C. Debus and P. H. Bolivar, Frequency selective surfaces for high sensitivity terahertz sensing, Appl. Phys. Lett. 91, 184102 (2007).
- 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).
- 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).
- https://www.refimeve.fr/index.php/en/.
The theoretical analysis toward the present experiment [24] assumes corresponding to the opposite magnetic field direction than applied in this work.
- 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).
- 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).
- N. F. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78, 695 (1950).
- N. F. Ramsey, Experiments with separated oscillatory fields and hydrogen masers, Rev. Mod. Phys. 62, 541 (1990).
- A. Nanda, Progress towards ramsey hyperfine spectroscopy in asacusa, in CPT and Lorentz Symmetry (World Scientific, Singapore, 2020), pp. 201–203.
- T. Schmidt, Über die magnetischen Momente der Atomkerne, Z. Phys. 106, 358 (1937).
- J. T. VanderPlas, Understanding the Lomb–Scargle periodogram, Astrophys. J. Suppl. Ser. 236, 16 (2018).
- J. T. VanderPlas and Željko Ivezić,Periodograms for multiband astronomical time series, Astrophys. J. 812, 18 (2015).
- 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).
- N. R. Lomb, Least-squares frequency analysis of unequally spaced data, Astrophys. Space Sci. 39, 447 (1976).
- J. D. Scargle,Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data, Astrophys. J. 263, 835 (1982).
- 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).
- 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).
- 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).
- 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).
- R. V. Baluev, Assessing the statistical significance of periodogram peaks, Mon. Not. R. Astron. Soc. 385, 1279 (2008).