- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

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

Ultralight scalar dark matter with off-diagonal flavor couplings

Jinhui Guo1,*, Jia Liu2,3,†, Chenhao Peng2,‡, Xiao-Ping Wang1,§, and Hang Zhao1,∥

  • *Contact author: guojh23@buaa.edu.cn
  • †Contact author: jialiu@pku.edu.cn
  • ‡Contact author: chenhaopeng@stu.pku.edu.cn
  • §Contact author: hcwangxiaoping@buaa.edu.cn
  • ∥Contact author: hangzhao@buaa.edu.cn
PDF

Phys. Rev. D 114, 015022 – Published 16 July, 2026

DOI: https://doi.org/10.1103/3c9n-gfvj

Abstract

Ultralight dark matter can behave as a coherent background field and induce time-dependent modifications of Standard Model parameters. We study a scenario in which a real ultralight scalar ϕ couples off-diagonally to down-type quarks, linking ultralight dark sectors to flavor physics. Working within an effective field theory, we diagonalize the quark mass matrix in a coherent ϕ background and derive analytic expressions for oscillatory shifts in down-type quark masses and Cabibbo-Kobayashi-Maskawa parameters. These effects lead to signatures in both the classical regime, where ϕ acts as a background field, and the quantum (particle) regime, where it contributes through on-shell production or off-shell mediation. Using precision flavor measurements, nuclear β decays, atomic-clock data, compiled NANOGrav-derived limits, and meson observables, we derive constraints on the flavor-violating couplings λij for mϕ∼10−24–10−12  eV, highlighting the complementarity of time-domain and flavor probes of ultralight dark sectors.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (92)

  1. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  2. V. C. Rubin and W. K. Ford, Jr., Rotation of the Andromeda Nebula from a spectroscopic survey of emission regions, Astrophys. J. 159, 379 (1970).
  3. E. G. M. Ferreira, Ultra-light dark matter, Astron. Astrophys. Rev. 29, 7 (2021).
  4. J.-P. Uzan, The fundamental constants and their variation: Observational status and theoretical motivations, Rev. Mod. Phys. 75, 403 (2003).
  5. 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).
  6. M. Battaglieri et al., US cosmic visions: New ideas in dark matter 2017: Community report, in U.S. Cosmic Visions: New Ideas in Dark Matter (2017), arXiv:1707.04591.
  7. D. Antypas et al., New horizons: Scalar and vector ultralight dark matter, arXiv:2203.14915.
  8. J.-P. Uzan, Varying constants, gravitation and cosmology, Living Rev. Relativity 14, 2 (2011).
  9. D. J. E. Marsh and S. Hoof, Astrophysical searches and constraints, The Search for Ultralight Bosonic Dark Matter (Springer, Cham, 2022).
  10. A. Arvanitaki, J. Huang, and K. Van Tilburg, Searching for dilaton dark matter with atomic clocks, Phys. Rev. D 91, 015015 (2015).
  11. 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).
  12. 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).
  13. M. Pospelov, S. Pustelny, M. P. Ledbetter, D. F. Jackson Kimball, W. Gawlik, and D. Budker, Detecting domain walls of axionlike models using terrestrial experiments, Phys. Rev. Lett. 110, 021803 (2013).
  14. A. Derevianko and M. Pospelov, Hunting for topological dark matter with atomic clocks, Nat. Phys. 10, 933 (2014).
  15. Y. V. Stadnik and V. V. Flambaum, Searches for topological defect dark matter via nongravitational signatures, Phys. Rev. Lett. 113, 151301 (2014).
  16. S. Sevillano Muñoz, A particle’s perspective on screening mechanisms, J. Cosmol. Astropart. Phys. 12 (2024) 052.
  17. N. Sherrill et al., Analysis of atomic-clock data to constrain variations of fundamental constants, New J. Phys. 25, 093012 (2023).
  18. A. Hees, J. Guéna, M. Abgrall, S. Bize, and P. Wolf, Searching for an oscillating massive scalar field as a dark matter candidate using atomic hyperfine frequency comparisons, Phys. Rev. Lett. 117, 061301 (2016).
  19. T. Damour and J. F. Donoghue, Equivalence principle violations and couplings of a light dilaton, Phys. Rev. D 82, 084033 (2010).
  20. K. Beloy et al. (BACON Collaboration), Frequency ratio measurements at 18-digit accuracy using an optical clock network, Nature (London) 591, 564 (2021).
  21. B. Elder, G. Mentasti, E. Pasatembou, C. F. A. Baynham, O. Buchmueller, C. R. Contaldi, C. de Rham, R. Hobson, and A. J. Tolley, Prospects for detecting new dark physics with the next generation of atomic clocks, Phys. Rev. D 112, 044053 (2025).
  22. C. Broggini, G. Di Carlo, L. Di Luzio, and C. Toni, Alpha radioactivity deep-underground as a probe of axion dark matter, Phys. Lett. B 855, 138836 (2024).
  23. V. F. Dmitriev and V. V. Flambaum, Limits on cosmological variation of quark masses and strong interaction, Phys. Rev. D 67, 063513 (2003).
  24. A. S. Göttel, A. Ejlli, K. Karan, S. M. Vermeulen, L. Aiello, V. Raymond, and H. Grote, Searching for scalar field dark matter with LIGO, Phys. Rev. Lett. 133, 101001 (2024).
  25. E. Hall and N. Aggarwal, Advanced LIGO, LISA, and cosmic explorer as dark matter transducers, arXiv:2210.17487.
  26. P. G. Thirolf, B. Seiferle, and L. von der Wense, The 229-thorium isomer: Doorway to the road from the atomic clock to the nuclear clock, J. Phys. B 52, 203001 (2019).
  27. P. G. Thirolf, S. Kraemer, D. Moritz, and K. Scharl, The thorium isomer Th229m: Review of status and perspectives after more than 50 years of research, Eur. Phys. J. Special Topics 233, 1113 (2024).
  28. J. Bovy, D. W. Hogg, and H.-W. Rix, Galactic masers and the Milky Way circular velocity, Astrophys. J. 704, 1704 (2009).
  29. P. F. de Salas and A. Widmark, Dark matter local density determination: Recent observations and future prospects, Rep. Prog. Phys. 84, 104901 (2021).
  30. H.-Y. Cheng and C.-W. Chiang, Revisiting scalar and pseudoscalar couplings with nucleons, J. High Energy Phys. 07 (2012) 009.
  31. F. Bishara, J. Brod, B. Grinstein, and J. Zupan, From quarks to nucleons in dark matter direct detection, J. High Energy Phys. 11 (2017) 059.
  32. P. Junnarkar and A. Walker-Loud, Scalar strange content of the nucleon from lattice QCD, Phys. Rev. D 87, 114510 (2013).
  33. Y.-B. Yang, A. Alexandru, T. Draper, J. Liang, and K.-F. Liu (xQCD Collaboration), πN and strangeness sigma terms at the physical point with chiral fermions, Phys. Rev. D 94, 054503 (2016).
  34. S. Durr et al., Lattice computation of the nucleon scalar quark contents at the physical point, Phys. Rev. Lett. 116, 172001 (2016).
  35. J. Ruiz de Elvira, M. Hoferichter, B. Kubis, and U.-G. Meißner, Extracting the σ-term from low-energy pion-nucleon scattering, J. Phys. G 45, 024001 (2018).
  36. M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U.-G. Meißner, High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations, Phys. Rev. Lett. 115, 092301 (2015).
  37. L. Alvarez-Ruso, T. Ledwig, J. Martin Camalich, and M. J. Vicente Vacas, Nucleon mass and pion-nucleon sigma term from a chiral analysis of lattice QCD world data, EPJ Web Conf. 73, 04015 (2014).
  38. A. Abdel-Rehim, C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, and A. Vaquero Aviles-Casco (ETM Collaboration), Direct evaluation of the quark content of nucleons from lattice QCD at the physical point, Phys. Rev. Lett. 116, 252001 (2016).
  39. M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U.-G. Meißner, Remarks on the pion–nucleon σ-term, Phys. Lett. B 760, 74 (2016).
  40. A. Crivellin, M. Hoferichter, and M. Procura, Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects, Phys. Rev. D 89, 054021 (2014).
  41. N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10, 531 (1963).
  42. M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
  43. I. Bigaran, P. J. Fox, Y. Gouttenoire, R. Harnik, G. Krnjaic, T. Menzo, and J. Zupan, Direct detection of ultralight dark matter via charged lepton flavor violation, Phys. Rev. Lett. 136, 251801 (2026).
  44. H. Banks and M. Mccullough, Charting the fifth force landscape, Phys. Rev. D 103, 075018 (2021).
  45. M. Bauer and G. Rostagni, Fifth forces from QCD axions scale differently, Phys. Rev. Lett. 132, 101802 (2024).
  46. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  47. C.-Y. Seng, High-precision determination of radiative corrections to superallowed nuclear beta decays, EPJ Web Conf. 342, 01025 (2025).
  48. P. D. Shidling et al., Precision half-life measurement of the β+ decay of K37, Phys. Rev. C 90, 032501 (2014).
  49. X. Zhang, N. Houston, and T. Li, Nuclear decay anomalies as a signature of axion dark matter, Phys. Rev. D 108, L071101 (2023).
  50. G. P. Centers et al., Stochastic fluctuations of bosonic dark matter, Nat. Commun. 12, 7321 (2021).
  51. T. Kobayashi et al., Search for ultralight dark matter from long-term frequency comparisons of optical and microwave atomic clocks, Phys. Rev. Lett. 129, 241301 (2022).
  52. C. J. Kennedy, E. Oelker, J. M. Robinson, T. Bothwell, D. Kedar, W. R. Milner, G. E. Marti, A. Derevianko, and J. Ye, Precision metrology meets cosmology: Improved constraints on ultralight dark matter from atom-cavity frequency comparisons, Phys. Rev. Lett. 125, 201302 (2020).
  53. S. Pommé et al., On decay constants and orbital distance to the Sun—part II: Beta minus decay, Metrologia 54, 19 (2016).
  54. I. Adachi et al. (Belle-II Collaboration), Evidence for B+→K+νν¯ decays, Phys. Rev. D 109, 112006 (2024).
  55. M. Hatsuda, and W. Siegel (NA62 Collaboration), Search for a feebly interacting particle X in the decay K+→π+X, J. High Energy Phys. 03 (2020) 058.
  56. J. Grygier et al. (Belle Collaboration), Search for B→hνν¯ decays with semileptonic tagging at Belle, Phys. Rev. D 96, 091101 (2017); 97, 099902(A) (2018).
  57. 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).
  58. C.-J. Dai and T. Li, Constraint on ultralight Nelson-Barr dark matter from time-dependent nuclear decay, Phys. Rev. D 112, 055001 (2025).
  59. A. Faessler, R. Hodak, S. Kovalenko, and F. Simkovic, Tritium and rhenium as a probe of cosmic neutrino background, J. Phys. G 38, 075202 (2011).
  60. L. Ubaldi, Effects of theta on the deuteron binding energy and the triple-alpha process, Phys. Rev. D 81, 025011 (2010).
  61. V. Bernard, N. Kaiser, and U.-G. Meissner, Aspects of chiral pion—nucleon physics, Nucl. Phys. A615, 483 (1997).
  62. D. Lee, U.-G. Meißner, K. A. Olive, M. Shifman, and T. Vonk, θ -dependence of light nuclei and nucleosynthesis, Phys. Rev. Res. 2, 033392 (2020).
  63. R. Brower, S. Chandrasekharan, J. W. Negele, and U. J. Wiese, QCD at fixed topology, Phys. Lett. B 560, 64 (2003).
  64. A. Bazavov et al. (MILC Collaboration), Results from the MILC collaboration’s SU(3) chiral perturbation theory analysis, Proc. Sci., LAT2009 (2009) 079 [arXiv:0910.3618].
  65. N. Fettes, U.-G. Meissner, and S. Steininger, Pion—nucleon scattering in chiral perturbation theory. 1. Isospin symmetric case, Nucl. Phys. A640, 199 (1998).
  66. M. Gattobigio, A. Kievsky, and M. Viviani, Energy spectra of small bosonic clusters having a large two-body scattering length, Phys. Rev. A 86, 042513 (2012).
  67. M. G. Kozlov and D. Budker, Comment on sensitivity coefficients to variation of fundamental constants, Ann. Phys. (Berlin) 531, 1800254 (2019).
  68. A. Afzal et al. (NANOGrav Collaboration), The NANOGrav 15 yr data set: Search for signals from new physics, Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  69. V. V. Flambaum, D. B. Leinweber, A. W. Thomas, and R. D. Young, Limits on the temporal variation of the fine structure constant, quark masses and strong interaction from quasar absorption spectra and atomic clock experiments, Phys. Rev. D 69, 115006 (2004).
  70. T. Rosenband et al., Frequency ratio of Al+ and Hg+ Single-ion optical clocks; metrology at the 17th decimal place, Science 319, 1154622 (2008).
  71. S. Bize et al., Testing the stability of fundamental constants with the Hg199+ single-ion optical clock, Phys. Rev. Lett. 90, 150802 (2003).
  72. N. Huntemann, M. Okhapkin, B. Lipphardt, S. Weyers, C. Tamm, and E. Peik, High-accuracy optical clock based on the octupole transition in Yb+171, Phys. Rev. Lett. 108, 090801 (2012).
  73. L. von der Wense and B. Seiferle, The Th229 isomer: Prospects for a nuclear optical clock, Eur. Phys. J. A 56, 277 (2020).
  74. A. J. Buras, J.-M. Gérard, and W. A. Bardeen, Large N approach to kaon decays and mixing 28 years later: ΔI=1/2 Rule, B^K and ΔMK, Eur. Phys. J. C 74, 2871 (2014).
  75. A. Kachanovich, U. Nierste, and I. Nišandžić, Higgs portal to dark matter and B→K(*) decays, Eur. Phys. J. C 80, 669 (2020).
  76. J. A. Bailey et al., B→Kl+l− decay form factors from three-flavor lattice QCD, Phys. Rev. D 93, 025026 (2016).
  77. N. Carrasco, P. Lami, V. Lubicz, L. Riggio, S. Simula, and C. Tarantino, K→π semileptonic form factors with Nf=2+1+1 twisted mass fermions, Phys. Rev. D 93, 114512 (2016).
  78. N. Gubernari, A. Kokulu, and D. van Dyk, B→P and B→V form factors from B-meson light-cone sum rules beyond leading twist, J. High Energy Phys. 01 (2018) 150.
  79. M. Bona et al. (UTfit Collaboration), Model-independent constraints on ΔF=2 operators and the scale of new physics, J. High Energy Phys. 03 (2008) 049.
  80. H.-M. Choi, C.-R. Ji, Z. Li, and H.-Y. Ryu, Variational analysis of mass spectra and decay constants for ground state pseudoscalar and vector mesons in the light-front quark model, Phys. Rev. C 92, 055203 (2015).
  81. P. A. Boyle, F. Erben, J. M. Flynn, N. Garron, J. Kettle, R. Mukherjee, and J. T. Tsang (RBC, UKQCD Collaborations), Kaon mixing beyond the standard model with physical masses, Phys. Rev. D 110, 034501 (2024).
  82. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG) Collaboration), FLAG review 2024, Phys. Rev. D 113, 014508 (2026).
  83. R. J. Dowdall, C. T. H. Davies, R. R. Horgan, G. P. Lepage, C. J. Monahan, J. Shigemitsu, and M. Wingate, Neutral B-meson mixing from full lattice QCD at the physical point, Phys. Rev. D 100, 094508 (2019).
  84. P. Touboul et al. (MICROSCOPE Collaboration), MICROSCOPE mission: Final results of the test of the equivalence principle, Phys. Rev. Lett. 129, 121102 (2022).
  85. Z. G. Berezhiani and M. Y. Khlopov, Physical and astrophysical consequences of cibreaking of the symmetry of families, Yad. Fiz. 51, 1479 (1990) (In Russian) [Sov. J. Nucl. Phys. 51, 935 (1990)].
  86. H. Davoudiasl and P. B. Denton, Ultralight boson dark matter and Event Horizon Telescope observations of M87*, Phys. Rev. Lett. 123, 021102 (2019).
  87. 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).
  88. L. Heurtier and Y. Zhang, Supernova constraints on massive (Pseudo)scalar coupling to neutrinos, J. Cosmol. Astropart. Phys. 02 (2016) 042.
  89. J. Jaber-Urquiza and I. A. Shovkovy, Scalar boson emission from a magnetized relativistic plasma, Phys. Rev. D 108, 096009 (2023).
  90. M. Salaris, S. Cassisi, R. P. Schiavon, and A. Pietrinferni, Effective temperatures of red giants in the apokasc catalogue and the mixing length calibration in stellar models, Astron. Astrophys. 612, A68 (2018).
  91. D. Saumon, S. Blouin, and P.-E. Tremblay, Current challenges in the physics of white dwarf stars, Phys. Rep. 988, 1 (2022).
  92. K. Hirata et al. (Kamiokande-II Collaboration), Observation of a neutrino burst from the Supernova SN 1987a, Phys. Rev. Lett. 58, 1490 (1987).

Outline

Information

Phys. Rev. D 114, 015022– Published 16 July, 2026
  • Received 2 April 2026
  • Accepted 29 June 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