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ηw-meson from topological properties of the electroweak vacuum

Gia Dvali1,2, Archil Kobakhidze3, and Otari Sakhelashvili2

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Phys. Rev. D 112, 093006 – Published 24 November, 2025

DOI: https://doi.org/10.1103/jc2g-q3nh

Abstract

We further scrutinize the evidence for a recently suggested pseudoscalar particle, the electroweak ηw meson. Its existence is demanded by matching the removal of the weak vacuum angle θw by the anomalous B+L symmetry with a massive pole in the topological susceptibility of the vacuum. We specifically focus on the possibility of the emergence of ηw as a collective excitation of the phase of the condensate of the ’t Hooft fermion determinant, generated by the electroweak instantons, which breaks the B+L symmetry spontaneously. We argue that the generation of the ’t Hooft vertex is in one-to-one correspondence with its nonzero vacuum expectation value which is cutoff insensitive. We outline certain puzzles about the nature of the emergent ηw which require further investigation.

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References (35)

  1. G. Dvali, A. Kobakhidze, and O. Sakhelashvili, Electroweak ηw meson, Phys. Rev. D 111, 11 (2025).
  2. G. Dvali, Three-form gauging of axion symmetries and gravity, arXiv:hep-th/0507215.
  3. G. Dvali, C. Gomez, and S. Zell, A proof of the axion? arXiv:1811.03079.
  4. G. Dvali, Strong-CP with and without gravity, arXiv:2209.14219.
  5. G. Dvali, The role of gravity in naturalness versus consistency: Strong-CP and dark energy, Phil. Trans. R. Soc. A 382, 20230084 (2023).
  6. G. Dvali, A. Kobakhidze, and O. Sakhelashvili, Hint to supersymmetry from the GR vacuum, Phys. Rev. D 110, 086008 (2024).
  7. G. Dvali, R. Jackiw, and S. Y. Pi, Topological mass generation in four dimensions, Phys. Rev. Lett. 96, 081602 (2006).
  8. G. Dvali, S. Folkerts, and A. Franca, How neutrino protects the axion, Phys. Rev. D 89, 105025 (2014).
  9. G. Dvali, Topological origin of chiral symmetry breaking in QCD and in gravity, arXiv:1705.06317.
  10. O. Sakhelashvili, Consistency of the dual formulation of axion solutions to the strong CP problem, Phys. Rev. D 105, 085020 (2022).
  11. G. ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14, 3432 (1976); 18, 2199 (1978).
  12. G. Dvali and L. Funcke, Small neutrino masses from gravitational θ-term, Phys. Rev. D 93, 113002 (2016).
  13. T. Eguchi and A. J. Hanson, Asymptotically flat selfdual solutions to euclidean gravity, Phys. Lett. 74B, 249 (1978).
  14. T. Eguchi and A. J. Hanson, Selfdual solutions to euclidean gravity, Ann. Phys. (N.Y.) 120, 82 (1979).
  15. A. A. Anselm and A. A. Johansen, Baryon nonconservation in standard model and Yukawa interaction, Nucl. Phys. B407, 313 (1993).
  16. A. A. Anselm and A. A. Johansen, Can electroweak theta term be observable?, Nucl. Phys. B412, 553 (1994).
  17. A. A. Anselm, Periodic universe and condensate of pseudoGoldstone field, Phys. Lett. B 260, 39 (1991).
  18. G. Dvali, G. Karananas, A. Kobakhidze, O. Sakhelashvili, and R. Wang (to be published).
  19. I. Affleck, On constrained instantons, Nucl. Phys. B191, 429 (1981).
  20. H. Georgi, L. Kaplan, and D. Morin, Nonperturbative matching for field theories with heavy fermions, Phys. Rev. D 49, 2457 (1994).
  21. G. Dvali and L. Eisemann, Perturbative understanding of nonperturbative processes and quantumization versus classicalization, Phys. Rev. D 106, 125019 (2022).
  22. G. Dvali, Unitarity entropy bound: Solitons and instantons, Fortschr. Phys. 69, 2000091 (2021).
  23. G. Dvali, Entropy bound and unitarity of scattering amplitudes, J. High Energy Phys. 03 (2021) 126.
  24. G. Dvali and C. Gomez, Black hole’s quantum N-portrait, Fortschr. Phys. 61, 742 (2013).
  25. G. Dvali, C. Gomez, R. S. Isermann, D. Lüst, and S. Stieberger, Black hole formation and classicalization in ultra-Planckian 2→N scattering, Nucl. Phys. B893, 187 (2015).
  26. A. Addazi, M. Bianchi, and G. Veneziano, Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions, J. High Energy Phys. 02 (2017) 111.
  27. L. Berezhiani, G. Dvali, and O. Sakhelashvili, Coherent states in gauge theories: Topological defects and other classical configurations, Phys. Rev. D 111, 065018 (2025).
  28. G. Dvali, Area law saturation of entropy bound from perturbative unitarity in renormalizable theories, Fortschr. Phys. 69, 2000090 (2021).
  29. E. Witten, Current algebra theorems for the U(1) Goldstone boson, Nucl. Phys. B156, 269 (1979).
  30. G. Veneziano, U(1) without instantons, Nucl. Phys. B159, 213 (1979).
  31. R. D. Pisarski and F. Rennecke, Multi-instanton contributions to anomalous quark interactions, Phys. Rev. D 101, 114019 (2020).
  32. N. V. Krasnikov, V. A. Rubakov, and V. F. Tokarev, Zero fermion modes in models with spontaneous symmetry breaking, J. Phys. A 12, L343 (1979).
  33. M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Am. Math. Soc. 69, 422 (1963).
  34. S. W. Hawking and C. N. Pope, Symmetry breaking by instantons in supergravity, Nucl. Phys. B146, 381 (1978).
  35. K. Konishi, N. Magnoli, and H. Panagopoulos, Spontaneous breaking of local supersymmetry by gravitational instantons, Nucl. Phys. B309, 201 (1988).

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Phys. Rev. D 112, 093006– Published 24 November, 2025
  • Received 24 September 2025
  • Accepted 9 November 2025
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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.

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