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

Torsion Balance Experiments Enable Direct Detection of Sub-eV Dark Matter

Shigeki Matsumoto1,*, Jie Sheng1,2,†, Chuan-Yang Xing3,‡, and Lin Zhu4,§

  • *Contact author: shigeki.matsumoto@ipmu.jp
  • †Contact author: jie.sheng@ipmu.jp
  • ‡Contact author: cyxing@upc.edu.cn
  • §Contact author: zhulin36@mail.hust.edu.cn

Phys. Rev. Lett. 136, 121803 – Published 26 March, 2026

DOI: https://doi.org/10.1103/8lbh-lblh

Abstract

Light dark matter with sub-eV masses has a high number density in our Galaxy, and its scattering cross section with macroscopic objects can be significantly enhanced by coherence effects. Repeated scattering with a target object can induce a measurable acceleration. Torsion balance experiments with geometric asymmetry are, in principle, capable of detecting such signals. Our analysis shows that existing torsion balances designed to test the equivalence principle already place the most stringent constraints on DM-nucleon scattering in the (10−2,1)  eV mass range.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (78)

  1. B.-L. Young, A survey of dark matter and related topics in cosmology, Front. Phys. (Beijing) 12, 121201 (2017); 12, 121202(E) (2017).
  2. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  3. G. Bertone, D. Hooper, and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rep. 405, 279 (2005).
  4. A. Arbey and F. Mahmoudi, Dark matter and the early Universe: A review, Prog. Part. Nucl. Phys. 119, 103865 (2021).
  5. M. W. Goodman and E. Witten, Detectability of certain dark matter candidates, Phys. Rev. D 31, 3059 (1985).
  6. T. Lin, Dark matter models and direct detection, Proc. Sci. 333 (2019) 009 [arXiv:1904.07915].
  7. J. Cooley, Dark matter direct detection of classical WIMPs, SciPost Phys. Lect. Notes 55 (2022), 10.21468/SciPostPhysLectNotes.55.
  8. J. Billard et al., Direct detection of dark matter—APPEC committee report, Rep. Prog. Phys. 85, 056201 (2022).
  9. D. S. Akerib et al., Snowmass2021 cosmic frontier dark matter direct detection to the neutrino fog, in Snowmass 2021 (2022), arXiv:2203.08084.
  10. R. Essig, J. Mardon, and T. Volansky, Direct detection of sub-GeV dark matter, Phys. Rev. D 85, 076007 (2012).
  11. S. Knapen, T. Lin, M. Pyle, and K. M. Zurek, Detection of light dark matter with optical phonons in polar materials, Phys. Lett. B 785, 386 (2018).
  12. S. Griffin, S. Knapen, T. Lin, and K. M. Zurek, Directional detection of light dark matter with polar materials, Phys. Rev. D 98, 115034 (2018).
  13. A. Coskuner, T. Trickle, Z. Zhang, and K. M. Zurek, Directional detectability of dark matter with single phonon excitations: Target comparison, Phys. Rev. D 105, 015010 (2022).
  14. B. Campbell-Deem, S. Knapen, T. Lin, and E. Villarama, Dark matter direct detection from the single phonon to the nuclear recoil regime, Phys. Rev. D 106, 036019 (2022).
  15. A. Mitridate, T. Trickle, Z. Zhang, and K. M. Zurek, Snowmass white paper: Light dark matter direct detection at the interface with condensed matter physics, Phys. Dark Universe 40, 101221 (2023).
  16. S.-F. Ge, J. Sheng, and C.-Y. Xing, Relativistic atomic effects of dark matter electron scattering, arXiv:2509.14534.
  17. G. Afek, D. Carney, and D. C. Moore, Coherent scattering of low mass dark matter from optically trapped sensors, Phys. Rev. Lett. 128, 101301 (2022).
  18. R. Essig et al., Snowmass2021 cosmic frontier: The landscape of low-threshold dark matter direct detection in the next decade, in Snowmass 2021 (2022), arXiv:2203.08297.
  19. C. G. Baker, W. P. Bowen, P. Cox, M. J. Dolan, M. Goryachev, and G. Harris, Optomechanical dark matter instrument for direct detection, Phys. Rev. D 110, 043005 (2024).
  20. K. A. Olive and M. Pospelov, Environmental dependence of masses and coupling constants, Phys. Rev. D 77, 043524 (2008).
  21. A. Hees, O. Minazzoli, E. Savalle, Y. V. Stadnik, and P. Wolf, Violation of the equivalence principle from light scalar dark matter, Phys. Rev. D 98, 064051 (2018).
  22. T. Bouley, P. Sørensen, and T.-T. Yu, Constraints on ultralight scalar dark matter with quadratic couplings, J. High Energy Phys. 03 (2023) 104.
  23. X. Gan, H. Kim, and A. Mitridate, Probing quadratically coupled ultralight dark matter with pulsar timing arrays, arXiv:2510.13945.
  24. A. Banerjee, G. Perez, M. Safronova, I. Savoray, and A. Shalit, The phenomenology of quadratically coupled ultra light dark matter, J. High Energy Phys. 10 (2023) 042.
  25. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  26. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  27. M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. 120B, 137 (1983).
  28. A. Derevianko and M. Pospelov, Hunting for topological dark matter with atomic clocks, Nat. Phys. 10, 933 (2014).
  29. Y. V. Stadnik and V. V. Flambaum, Improved limits on interactions of low-mass spin-0 dark matter from atomic clock spectroscopy, Phys. Rev. A 94, 022111 (2016).
  30. T. Kalaydzhyan and N. Yu, Extracting dark matter signatures from atomic clock stability measurements, Phys. Rev. D 96, 075007 (2017).
  31. X. Zhang, A. Banerjee, M. Leyser, G. Perez, S. Schiller, D. Budker, and D. Antypas, Search for ultralight dark matter with spectroscopy of radio-frequency atomic transitions, Phys. Rev. Lett. 130, 251002 (2023).
  32. Y. V. Stadnik and V. V. Flambaum, Searching for dark matter and variation of fundamental constants with laser and maser interferometry, Phys. Rev. Lett. 114, 161301 (2015).
  33. H. Masia-Roig et al., Intensity interferometry for ultralight bosonic dark matter detection, Phys. Rev. D 108, 015003 (2023).
  34. Y. V. Stadnik and V. V. Flambaum, Searches for topological defect dark matter via nongravitational signatures, Phys. Rev. Lett. 113, 151301 (2014).
  35. Y. V. Stadnik and V. V. Flambaum, Can dark matter induce cosmological evolution of the fundamental constants of nature?, Phys. Rev. Lett. 115, 201301 (2015).
  36. Y. V. Stadnik and V. V. Flambaum, Constraining scalar dark matter with big bang nucleosynthesis and atomic spectroscopy, arXiv:1504.01798.
  37. D. Blas, D. L. Nacir, and S. Sibiryakov, Ultralight dark matter resonates with binary pulsars, Phys. Rev. Lett. 118, 261102 (2017).
  38. D. Blas, D. López Nacir, and S. Sibiryakov, Secular effects of ultralight dark matter on binary pulsars, Phys. Rev. D 101, 063016 (2020).
  39. C. Dailey, C. Bradley, D. F. Jackson Kimball, I. A. Sulai, S. Pustelny, A. Wickenbrock, and A. Derevianko, Quantum sensor networks as exotic field telescopes for multi-messenger astronomy, Nat. Astron. 5, 150 (2021).
  40. J. F. Acevedo, A. J. Reilly, and L. Santos-Olmsted, Dark drag around Sagittarius A*, arXiv:2510.01320.
  41. Y. V. Stadnik, Searching for ultralight scalar dark matter with muonium and muonic atoms, Phys. Rev. Lett. 131, 011001 (2023).
  42. H. Fukuda, S. Matsumoto, and T. T. Yanagida, Direct detection of ultralight dark matter via astronomical ephemeris, Phys. Lett. B 789, 220 (2019).
  43. H. Fukuda and S. Shirai, Detection of QCD axion dark matter by coherent scattering, Phys. Rev. D 105, 095030 (2022).
  44. P. Luo, S. Matsumoto, J. Sheng, C.-Y. Xing, L. Zhu, and Z.-J. Zhuge, Detecting meV-scale dark matter via coherent scattering with an asymmetric torsion balance, Phys. Rev. D 112, 075023 (2025).
  45. V. Domcke and M. Spinrath, Detection prospects for the cosmic neutrino background using laser interferometers, J. Cosmol. Astropart. Phys. 06 (2017) 055.
  46. P. W. Graham, D. E. Kaplan, J. Mardon, S. Rajendran, and W. A. Terrano, Dark matter direct detection with accelerometers, Phys. Rev. D 93, 075029 (2016).
  47. D. Carney, A. Hook, Z. Liu, J. M. Taylor, and Y. Zhao, Ultralight dark matter detection with mechanical quantum sensors, New J. Phys. 23, 023041 (2021).
  48. H. Day, D. Liu, M. A. Luty, and Y. Zhao, Blowing in the dark matter wind, J. High Energy Phys. 07 (2024) 136.
  49. A. Arcusa et al. (IAXO Collaboration), The International Axion Observatory (IAXO): Case, status and plans. Input to the European strategy for particle physics, arXiv:2504.00079.
  50. J. Jaeckel and J. Redondo, Resonant to broadband searches for cold dark matter consisting of weakly interacting slim particles, Phys. Rev. D 88, 115002 (2013).
  51. J. Egge et al. (MADMAX Collaboration), First search for dark photon dark matter with a madmax prototype, Phys. Rev. Lett. 134, 151004 (2025).
  52. J. Chiles et al., New constraints on dark photon dark matter with superconducting nanowire detectors in an optical haloscope, Phys. Rev. Lett. 128, 231802 (2022).
  53. D. Baxter et al., Recommended conventions for reporting results from direct dark matter searches, Eur. Phys. J. C 81, 907 (2021).
  54. D. Akimov et al. (COHERENT Collaboration), Observation of coherent elastic neutrino-nucleus scattering, Science 357, 1123 (2017).
  55. P. G. Roll, R. Krotkov, and R. H. Dicke, The equivalence of inertial and passive gravitational mass, Ann. Phys. (N.Y.) 26, 442 (1964).
  56. V. B. Braginskii and V. I. Panov, Verification of equivalence of inertial and gravitational masses, Sov. Phys. JETP 34, 463 (1972), http://www.jetp.ras.ru//cgi-bin/e/index/e/34/3/p463?a=list.
  57. Y. Su, B. R. Heckel, E. G. Adelberger, J. H. Gundlach, M. Harris, G. L. Smith, and H. E. Swanson, New tests of the universality of free fall, Phys. Rev. D 50, 3614 (1994).
  58. S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, Test of the equivalence principle using a rotating torsion balance, Phys. Rev. Lett. 100, 041101 (2008).
  59. T. A. Wagner, S. Schlamminger, J. H. Gundlach, and E. G. Adelberger, Torsion-balance tests of the weak equivalence principle, Classical Quantum Gravity 29, 184002 (2012).
  60. E. A. Shaw, M. P. Ross, C. A. Hagedorn, E. G. Adelberger, and J. H. Gundlach, Torsion-balance search for ultralow-mass bosonic dark matter, Phys. Rev. D 105, 042007 (2022).
  61. P. Sikivie, Invisible axion search methods, Rev. Mod. Phys. 93, 015004 (2021).
  62. A. Caputo, A. J. Millar, C. A. J. O’Hare, and E. Vitagliano, Dark photon limits: A handbook, Phys. Rev. D 104, 095029 (2021).
  63. K. Li et al., Neutron limit on the strongly-coupled chameleon field, Phys. Rev. D 93, 062001 (2016).
  64. B. Elder, J. Khoury, P. Haslinger, M. Jaffe, H. Müller, and P. Hamilton, Chameleon dark energy and atom interferometry, Phys. Rev. D 94, 044051 (2016).
  65. G. Cronenberg, P. Brax, H. Filter, P. Geltenbort, T. Jenke, G. Pignol, M. Pitschmann, M. Thalhammer, and H. Abele, Acoustic Rabi oscillations between gravitational quantum states and impact on symmetron dark energy, Nat. Phys. 14, 1022 (2018).
  66. See Supplemental Material at http://link.aps.org/supplemental/10.1103/8lbh-lblh for further details.
  67. G. G. Raffelt, Stars as laboratories for fundamental physics: The astrophysics of neutrinos, axions, and other weakly interacting particles (University of Chicago Press, Chicago, 1996).
  68. K. Van Tilburg, Wake forces in a background of quadratically coupled mediators, Phys. Rev. D 109, 096036 (2024).
  69. S. Barbosa and S. Fichet, Background-induced forces from dark relics, J. High Energy Phys. 01 (2025) 021.
  70. Y. Grossman, B. Yu, and S. Zhou, Axion forces in axion backgrounds, J. High Energy Phys. 01 (2026) 145.
  71. Y. Cheng and S. Ge, Background-enhanced axion force by axion dark matter, arXiv:2504.02702.
  72. X. Gan, D. Liu, D. Liu, X. Luo, and B. Yu, Detecting ultralight dark matter with matter effect, J. High Energy Phys. 02 (2026) 043.
  73. W.-H. Tan et al., Improvement for testing the gravitational inverse-square law at the submillimeter range, Phys. Rev. Lett. 124, 051301 (2020).
  74. C. V. Cappiello, K. C. Y. Ng, and J. F. Beacom, Reverse direct detection: Cosmic ray scattering with light dark matter, Phys. Rev. D 99, 063004 (2019).
  75. T. Bringmann and M. Pospelov, Novel direct detection constraints on light dark matter, Phys. Rev. Lett. 122, 171801 (2019).
  76. X. Cui et al. (PandaX-II Collaboration), Search for cosmic-ray boosted sub-GeV dark matter at the PandaX-II experiment, Phys. Rev. Lett. 128, 171801 (2022).
  77. K. Abe et al. (Super-Kamiokande Collaboration), Search for cosmic-ray boosted sub-GeV dark matter using recoil protons at Super-Kamiokande, Phys. Rev. Lett. 130, 031802 (2023); 131, 159903(E) (2023).
  78. J. Aalbers et al. (LZ Collaboration), New constraints on cosmic ray-boosted dark matter from the LUX-ZEPLIN experiment, Phys. Rev. Lett. 134, 241801 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation