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

Constraints on New Vector Boson Mediated Electron-Nucleus Interactions from Spectroscopy Data of Polar Diatomic Molecules

Konstantin Gaul1,2,3,*, Lei Cong1,2,3,†, and Dmitry Budker1,2,3,4

  • *Contact author: konstantin.gaul@uni-mainz.de
  • †Contact author: conglei1@uni-mainz.de

Phys. Rev. Lett. 136, 181805 – Published 6 May, 2026

DOI: https://doi.org/10.1103/d19m-s856

Abstract

A measurement of parity violation in the hyperfine structure of Ba138F19 [E. Altuntaş et al. Phys. Rev. Lett. 120, 142501 (2018)] is reinterpreted with electronic structure calculations in terms of beyond standard model vector boson mediated electron-nucleus interactions. Our results set constraints on previously unexplored, new boson mediated axial vector-vector nucleus-electron interactions. Similar bounds are obtained by analyzing the atomic parity violation experiment with Cs133. Moreover, we show that future experiments with cold heavy diatomic molecules like BaF137 or RaF225 can improve the present sensitivity to axial vector-vector nucleus-electron and nucleon-nucleus interactions by at least 2 orders of magnitude for large boson masses.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (95)

  1. T. D. Lee and C. N. Yang, Question of parity conservation in weak interactions, Phys. Rev. 104, 254 (1956).
  2. C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson, Experimental test of parity conservation in beta decay, Phys. Rev. 105, 1413 (1957).
  3. J. Jaeckel and A. Ringwald, The low-energy frontier of particle physics, Annu. Rev. Nucl. Part. Sci. 60, 405 (2010).
  4. M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90, 025008 (2018).
  5. G. Bertone and D. Hooper, History of dark matter, Rev. Mod. Phys. 90, 045002 (2018).
  6. G. Bertone, D. Hooper, and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rep. 405, 279 (2005).
  7. L. Cong, W. Ji, P. Fadeev, F. Ficek, M. Jiang, V. V. Flambaum, H. Guan, D. F. Jackson Kimball, M. G. Kozlov, Y. V. Stadnik, and D. Budker, Spin-dependent exotic interactions, Rev. Mod. Phys. 97, 025005 (2025).
  8. A. Arza, D. Aybas, S. Balaji, R. Balkin, K. Bartnick, C. F. A. Baynham, I. M. Bloch, C. Bonati, D. Budker, C. Burrage, M. Buschmann, F. Calore, F. R. Candón, P. Carenza, S. A. Cetin, F. Chadha-Day, S. Chakraborti, K. Choi, M. Cicoli, L. Cong et al., The cosmic wispers white paper: The physics case for weakly interacting slim particles, arXiv:2603.03433.
  9. J. L. Lopez, String unification and leptophobic Z′ in flipped SU(5), Nucl. Phys. B, Proc. Suppl. 52, 284 (1997).
  10. D. Gómez Dumm, Leptophobic character of the Z′ in an SU(3)C⊗SU(3)L⊗U(1)X model, Phys. Lett. B 411, 313 (1997).
  11. T. G. Rizzo, Gauge kinetic mixing and leptophobic Z′ in E6 and SO(10), Phys. Rev. D 59, 015020 (1998).
  12. S. Baek, J. H. Jeon, and C. Kim, Bs0−B¯s0 mixing in leptophobic Z′ model, Phys. Lett. B 641, 183 (2006).
  13. B. Shuve and I. Yavin, Dark matter progenitor: Light vector boson decay into sterile neutrinos, Phys. Rev. D 89, 113004 (2014).
  14. A. Alves, S. Profumo, and F. S. Queiroz, The dark Z’ portal: Direct, indirect and collider searches, J. High Energy Phys. 04 (2014) 063.
  15. M. Hostert, M. Pospelov, and A. Thompson, Kaon decay constraints on vector bosons coupled to non-conserved currents, arXiv:2602.19479.
  16. M. Hostert and M. Pospelov, Pion decay constraints on exotic 17 MeV vector bosons, Phys. Rev. D 108, 055011 (2023).
  17. A. J. Krasznahorkay, Observation of anomalous internal pair creation in Be8: A possible indication of a light, neutral boson, Phys. Rev. Lett. 116, 042501 (2016).
  18. C. J. G. Mommers and M. Vanderhaeghen, Constraining the axial-vector X17 interpretation with C12 data, Phys. Lett. B 858, 139031 (2024).
  19. 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).
  20. K. Tsigutkin, D. Dounas-Frazer, A. Family, J. E. Stalnaker, V. V. Yashchuk, and D. Budker, Observation of a large atomic parity violation effect in ytterbium, Phys. Rev. Lett. 103, 071601 (2009).
  21. 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).
  22. P. A. Vetter, D. M. Meekhof, P. K. Majumder, S. K. Lamoreaux, and E. N. Fortson, Precise test of electroweak theory from a new measurement of parity nonconservation in atomic thallium, Phys. Rev. Lett. 74, 2658 (1995).
  23. A. T. Nguyen, D. Budker, D. DeMille, and M. Zolotorev, Search for parity nonconservation in atomic dysprosium, Phys. Rev. A 56, 3453 (1997).
  24. N. Leefer, L. Bougas, D. Antypas, and D. Budker, Towards a new measurement of parity violation in dysprosium, arXiv:1412.1245.
  25. 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).
  26. L. N. Labzowsky, Λ-doubling and parity-nonconservation effects in spectra of diatomic molecules, Sov. Phys. JETP 48, 434 (1978), https://www.jetp.ras.ru/cgi-bin/e/index/e/48/3/p434?a=list.
  27. O. P. Sushkov and V. V. Flambaum, Parity breaking effects in diatomic molecules, Sov. Phys. JETP 48, 608 (1978), https://www.jetp.ras.ru/cgi-bin/e/index/e/48/4/p608?a=list.
  28. M. G. Kozlov and L. N. Labzowsky, Parity violation effects in diatomics, J. Phys. B 28, 1933 (1995).
  29. I. B. Khriplovich, Fundamental symmetries and atomic physics, Phys. Scr. T 112, 52 (2004).
  30. A. V. Titov, N. S. Mosyagin, A. N. Petrov, T. A. Isaev, and D. P. DeMille, Study of P,T-parity violation effects in polar heavy-atom molecules, Prog. Theor. Chem. Phys. B 15, 253 (2006).
  31. 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).
  32. R. Berger and J. Stohner, Parity violation, Wiley Interdiscip. Rev.-Comput. Mol. Sci. 9, e1396 (2019).
  33. D. DeMille, S. B. Cahn, D. Murphree, D. A. Rahmlow, and M. G. Kozlov, Using molecules to measure nuclear spin-dependent parity violation, Phys. Rev. Lett. 100, 023003 (2008).
  34. T. A. Isaev, S. Hoekstra, and R. Berger, Laser-cooled RaF as a promising candidate to measure molecular parity violation, Phys. Rev. A 82, 052521 (2010).
  35. T. A. Isaev and R. Berger, Electron correlation and nuclear charge dependence of parity-violating properties in open-shell diatomic molecules, Phys. Rev. A 86, 062515 (2012).
  36. T. A. Isaev and R. Berger, Periodic trends in parity-violating hyperfine coupling constants of open-shell diatomic molecules, J. Mol. Spectrosc. 300, 26 (2014).
  37. A. Borschevsky, M. Ilias, V. A. Dzuba, V. V. Flambaum, and P. Schwerdtfeger, Relativistic study of nuclear-anapole-moment effects in diatomic molecules, Phys. Rev. A 88, 022125 (2013).
  38. E. Altuntaş, J. Ammon, S. B. Cahn, and D. DeMille, Demonstration of a sensitive method to measure nuclear-spin-dependent parity violation, Phys. Rev. Lett. 120, 142501 (2018).
  39. J. Karthein, S. M. Udrescu, S. B. Moroch, I. Belosevic, K. Blaum, A. Borschevsky, Y. Chamorro, D. DeMille, J. Dilling, R. F. Garcia Ruiz, N. R. Hutzler, L. F. Pašteka, and R. Ringle, Electroweak nuclear properties from single molecular ions in a penning trap, Phys. Rev. Lett. 133, 033003 (2024).
  40. L. Hunter, J. Gordon, S. Peck, D. Ang, and J.-F. Lin, Using the earth as a polarized electron source to search for long-range spin-spin interactions, Science 339, 928 (2013).
  41. Y. Wang, Y. Huang, C. Guo, M. Jiang, X. Kang, H. Su, Y. Qin, W. Ji, D. Hu, X. Peng, and D. Budker, Search for exotic parity-violation interactions with quantum spin amplifiers, Sci. Adv. 9, eade0353 (2023).
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/d19m-s856 for computational details, which includes Refs. [7,25,34,35,43–71] and numerical values for all contributions to parity-violating matrix elements in all studied molecules for different boson masses. In addition, we present an extended discussion of the impact of nuclear theory uncertainties on constraints on new bosons from molecular spectroscopy.
  43. R. Berger, N. Langermann, and C. van Wüllen, Zeroth order regular approximation approach to molecular parity violation, Phys. Rev. A 71, 042105 (2005).
  44. S. Nahrwold and R. Berger, Zeroth order regular approximation approach to parity violating nuclear magnetic resonance shielding tensors, J. Chem. Phys. 130, 214101 (2009).
  45. K. Gaul and R. Berger, Toolbox approach for quasi-relativistic calculation of molecular properties for precision tests of fundamental physics, J. Chem. Phys. 152, 044101 (2020).
  46. M. T. Colombo Jofré, K. Kozioł, I. A. Aucar, K. Gaul, R. Berger, and G. A. Aucar, Relativistic and QED corrections to one-bond indirect nuclear spin–spin couplings in X22+ and X32+ ions (X=Zn, Cd, Hg), J. Chem. Phys. 157, 064103 (2022).
  47. C. Zülch, K. Gaul, S. M. Giesen, R. F. G. Ruiz, and R. Berger, Cool molecular highly charged ions for precision tests of fundamental physics, arXiv:2203.10333.
  48. S. A. Brück, N. Sahu, K. Gaul, and R. Berger, Quasi-relativistic approach to analytical gradients of parity violating potentials, J. Chem. Phys. 158, 194109 (2023).
  49. C. van Wüllen, Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations, J. Chem. Phys. 109, 392 (1998).
  50. C. van Wüllen, A quasirelativistic two-component density functional and Hartree-Fock program, Z. Phys. Chem. 224, 413 (2010).
  51. R. Ahlrichs, M. Bär, M. Häser, H. Horn, and C. Kölmel, Electronic structure calculations on workstation computers: The program system turbomole, Chem. Phys. Lett. 162, 165 (1989).
  52. K. Gaul and R. Berger, Global analysis of CP-violation in atoms, molecules and role of medium-heavy systems, J. High Energy Phys. 08 (2024) 100.
  53. P. A. M. Dirac, Note on exchange phenomena in the Thomas atom, Proc. Cambridge Philos. Soc. 26, 376 (1930).
  54. J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev. 81, 385 (1951).
  55. S. H. Vosko, L. Wilk, and M. Nuisar, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis, Can. J. Phys. 58, 1200 (1980).
  56. K. G. Dyall, Relativistic quadruple-zeta and revised triple-zeta and double-zeta basis sets for the 4p, 5p, and 6p elements, Theor. Chem. Acc. 115, 441 (2006).
  57. V. V. Flambaum and I. B. Khriplovich, Nuclear anapole moments, Phys. Lett. 146B, 367 (1984).
  58. G. G. Raffelt, Particle physics from stars, Annu. Rev. Nucl. Part. Sci. 49, 163 (1999).
  59. J. A. Dror, R. Lasenby, and M. Pospelov, New constraints on light vectors coupled to anomalous currents, Phys. Rev. Lett. 119, 141803 (2017).
  60. C. Delaunay, C. Frugiuele, E. Fuchs, and Y. Soreq, Probing new spin-independent interactions through precision spectroscopy in atoms with few electrons, Phys. Rev. D 96, 115002 (2017).
  61. F. Ficek, D. F. J. Kimball, M. G. Kozlov, N. Leefer, S. Pustelny, and D. Budker, Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopy, Phys. Rev. A 95, 032505 (2017).
  62. N. F. Ramsey, The tensor force between two protons at long range, Physica (Amsterdam) 96A, 285 (1979).
  63. V. V. Flambaum and I. B. Khriplovich, On the enhancement of parity nonconserving effects in diatomic molecules, Phys. Lett. 110A, 121 (1985).
  64. P. Fadeev and V. V. Flambaum, Time-reversal invariance violation in neutron-nucleus scattering, Phys. Rev. C 100, 015504 (2019).
  65. W. Liu, C. van Wüllen, F. Wang, and L. Li, Spectroscopic constants of MH and M2 (M=Tl, E113, Bi, E115): Direct comparisons of four- and two-component approaches in the framework of relativistic density functional theory, J. Chem. Phys. 116, 3626 (2002).
  66. A. D. Becke, A new mixing of Hartree-Fock and local density-functional theories, J. Chem. Phys. 98, 1372 (1993).
  67. L. Visscher and K. G. Dyall, Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions, At. Data Nucl. Data Tables 67, 207 (1997).
  68. N. Stone, Table of nuclear magnetic dipole and electric quadrupole moments, At. Data Nucl. Data Tables 90, 75 (2005).
  69. A. N. Moskalev, R. M. Ryndin, and I. B. Khriplovich, Possible lines of research into weak-interaction effects in atomic physics, Sov. Phys. Usp. 19, 220 (1976).
  70. I. Malkin, O. L. Malkina, V. G. Malkin, and M. Kaupp, Relativistic two-component calculations of electronic g-tensors that include spin polarization, J. Chem. Phys. 123, 244103 (2005).
  71. K. Gaul and R. Berger, Ab initio study of parity and time-reversal violation in laser-coolable triatomic molecules, Phys. Rev. A 101, 012508 (2020).
  72. P. Fadeev, Y. V. Stadnik, F. Ficek, M. G. Kozlov, V. V. Flambaum, and D. Budker, Revisiting spin-dependent forces mediated by new bosons: Potentials in the coordinate-space representation for macroscopic- and atomic-scale experiments, Phys. Rev. A 99, 022113 (2019).
  73. A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
  74. Y. Hao, M. Iliaš, E. Eliav, P. Schwerdtfeger, V. V. Flambaum, and A. Borschevsky, Nuclear anapole moment interaction in baf from relativistic coupled-cluster theory, Phys. Rev. A 98, 032510 (2018).
  75. A. D. Kudashov, A. N. Petrov, L. V. Skripnikov, N. S. Mosyagin, T. A. Isaev, R. Berger, and A. V. Titov, Ab initio study of radium monofluoride (RaF) as a candidate to search for parity- and time-and-parity violation effects, Phys. Rev. A 90, 052513 (2014).
  76. S. G. Wilkins et al., Observation of the distribution of nuclear magnetization in a molecule, Science 390, adm7717 (2025).
  77. L. Cong, W. Ji, and D. Budker, Fifth force limits, Zenodo, 2025, 10.5281/zenodo.14572652.
  78. V. V. Flambaum and D. W. Murray, Anapole moment and nucleon weak interactions, Phys. Rev. C 56, 1641 (1997).
  79. C. Baruch, P. B. Changala, Y. Shagam, and Y. Soreq, Constraining P and T violating forces with chiral molecules, Phys. Rev. Res. 6, 043115 (2024).
  80. F. Kogel, T. Garg, M. Rockenhäuser, and T. Langen, Laser cooled BaF137 molecules for measuring nuclear-spin-dependent parity violation, Phys. Rev. Res. 7, L022041 (2025).
  81. F. Kogel, T. Garg, M. Rockenhäuser, S. A. Morales-Ramírez, and T. Langen, Isotopologue-selective laser cooling of molecules, New J. Phys. 27, 013001 (2025).
  82. T. A. Isaev and R. Berger, Lasercooled radium monofluoride: A molecular all-in-one probe for new physics, arXiv:1302.5682.
  83. R. F. Garcia Ruiz et al., Spectroscopy of short-lived radioactive molecules, Nature (London) 581, 396 (2020).
  84. S. M. Udrescu et al., Isotope shifts of radium monofluoride molecules, Phys. Rev. Lett. 127, 033001 (2021).
  85. S. M. Udrescu et al., Precision spectroscopy and laser-cooling scheme of a radium-containing molecule, Nat. Phys. 20, 202 (2024).
  86. K. Gaul, R. F. Garcia Ruiz, and R. Berger, Stopping mass-selected alkaline-earth metal monofluoride beams of high energy via formation of unusually stable anions, arXiv:2403.09320.
  87. Y. Hao, P. Navrátil, E. B. Norrgard, M. Iliaš, E. Eliav, R. G. E. Timmermans, V. V. Flambaum, and A. Borschevsky, Nuclear spin-dependent parity-violating effects in light polyatomic molecules, Phys. Rev. A 102, 052828 (2020).
  88. T. Chupp and M. Ramsey-Musolf, Electric dipole moments: A global analysis, Phys. Rev. C 91, 035502 (2015).
  89. S. Degenkolb, N. Elmer, T. Modak, M. Mühlleitner, and T. Plehn, A global view of the EDM landscape, arXiv:2403.02052.
  90. J. W. Blanchard, D. Budker, D. DeMille, M. G. Kozlov, and L. V. Skripnikov, Using parity-nonconserving spin-spin coupling to measure the Tl nuclear anapole moment in a TlF molecular beam, Phys. Rev. Res. 5, 013191 (2023).
  91. E. Van Dyke, J. Eills, K. Sheberstov, J. Blanchard, M. Wagner, A. E. Wedenig, K. Gaul, R. Berger, R. Pietschnig, D. Kargin, D. A. Barskiy, and D. Budker, Towards detection of molecular parity violation via chiral co-sensing: The H1/P31 model system, Phys. Chem. Chem. Phys. 27, 6092 (2025).
  92. K. Gaul, M. G. Kozlov, T. A. Isaev, and R. Berger, Chiral molecules as sensitive probes for direct detection of P-odd cosmic fields, Phys. Rev. Lett. 125, 123004 (2020).
  93. K. Gaul, M. G. Kozlov, T. A. Isaev, and R. Berger, Parity nonconserving interactions of electrons in chiral molecules with cosmic fields, Phys. Rev. A 102, 032816 (2020).
  94. www.ahrp.info.
  95. https://zenodo.org/records/19664873.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation