- 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
  • Letter
  • Open Access

First-order electroweak phase transition with a gauge-invariant approach

Renhui Qin1 and Ligong Bian1,2,*

  • 1Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China
  • 2Center for High Energy Physics, Peking University, Beijing 100871, China

  • *Contact author: lgbycl@cqu.edu.cn
PDF

Phys. Rev. D 111, L051702 – Published 31 March, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L051702

Abstract

We study the electroweak phase transition with a three-dimensional standard model effective field theory at the two-loop level under a gauge-invariant approach. We observe that the phase transition parameters obtained with the gauge-invariant approach deviate from that obtained in the Landau gauge at around the percent level. We give the strongly first-order phase transition condition for electroweak baryogenesis and find that the predicted gravitational wave signals would be reduced for the new physics scale Λ≲590  GeV, and the parameter spaces of Λ≲570  GeV can be probed by the space-based interferometers, such as LISA, TianQin, and Taiji.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. 14, 125003 (2012).
  2. J. Yang and L. Bian, Phys. Rev. D 106, 023510 (2022).
  3. Y. Di, J. Wang, R. Zhou, L. Bian, R.-G. Cai, and J. Liu, Phys. Rev. Lett. 126, 251102 (2021).
  4. Y. Zhang, T. Vachaspati, and F. Ferrer, Phys. Rev. D 100, 083006 (2019).
  5. T. Stevens, M. B. Johnson, L. S. Kisslinger, and E. M. Henley, Phys. Rev. D 85, 063003 (2012).
  6. T. Kahniashvili, A. G. Tevzadze, and B. Ratra, Astrophys. J. 726, 78 (2011).
  7. M. Hindmarsh and A. Everett, Phys. Rev. D 58, 103505 (1998).
  8. D. Grasso and A. Riotto, Phys. Lett. B 418, 258 (1998).
  9. J. Ahonen and K. Enqvist, Phys. Rev. D 57, 664 (1998).
  10. R. Roshan and G. White, Rev. Mod. Phys. 97, 015001 (2025).
  11. P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Prog. Part. Nucl. Phys. 135, 104094 (2024).
  12. C. Caprini et al., J. Cosmol. Astropart. Phys. 04 (2016) 001.
  13. M. D’Onofrio, K. Rummukainen, and A. Tranberg, Phys. Rev. Lett. 113, 141602 (2014).
  14. Y. Hu, Phys. Rev. D 54, 1614 (1996).
  15. H. H. Patel and M. J. Ramsey-Musolf, J. High Energy Phys. 07 (2011) 029.
  16. N. K. Nielsen, Nucl. Phys. B101, 173 (1975).
  17. M. Garny and T. Konstandin, J. High Energy Phys. 07 (2012) 189.
  18. J. Hirvonen, J. Löfgren, M. J. Ramsey-Musolf, P. Schicho, and T. V. I. Tenkanen, J. High Energy Phys. 07 (2022) 135.
  19. J. Löfgren, M. J. Ramsey-Musolf, P. Schicho, and T. V. I. Tenkanen, Phys. Rev. Lett. 130, 251801 (2023).
  20. P. Schicho, T. V. I. Tenkanen, and G. White, J. High Energy Phys. 11 (2022) 047.
  21. L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Phys. Rev. Lett. 126, 171802 (2021).
  22. D. Croon, O. Gould, P. Schicho, T. V. I. Tenkanen, and G. White, J. High Energy Phys. 04 (2021) 055.
  23. P. Athron, C. Balazs, A. Fowlie, L. Morris, G. White, and Y. Zhang, J. High Energy Phys. 01 (2023) 050.
  24. W. Buchmuller, Z. Fodor, and A. Hebecker, Phys. Lett. B 331, 131 (1994).
  25. A. Hebecker, The electroweak phase transition, Other thesis, 1995, arXiv:hep-ph/9506418.
  26. W. Buchmuller, Z. Fodor, and A. Hebecker, Nucl. Phys. B447, 317 (1995).
  27. K. Farakos, K. Kajantie, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B425, 67 (1994).
  28. K. Farakos, K. Kajantie, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B442, 317 (1995).
  29. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B458, 90 (1996).
  30. A. Gynther, Phys. Rev. D 68, 016001 (2003).
  31. M. Laine, Phys. Rev. D 51, 4525 (1995).

  32. It has been established that the 3D thermal SMEFT at two-loop level will reduce the renormalization scale dependence fairly well [22, 23]. For the research with 4d SMEFT, see [33, 34, 35, 36, 37, 38, 39, 40].

  33. R.-G. Cai, M. Sasaki, and S.-J. Wang, J. High Energy Phys. 08 (2017) 004.
  34. C. Grojean, G. Servant, and J. D. Wells, Phys. Rev. D 71, 036001 (2005).
  35. C. Delaunay, C. Grojean, and J. D. Wells, J. High Energy Phys. 04 (2008) 029.
  36. M. Chala, C. Krause, and G. Nardini, J. High Energy Phys. 07 (2018) 062.
  37. D. Bodeker, L. Fromme, S. J. Huber, and M. Seniuch, J. High Energy Phys. 02 (2005) 026.
  38. K. Hashino and D. Ueda, Phys. Rev. D 107, 095022 (2023).
  39. P. H. Damgaard, A. Haarr, D. O’Connell, and A. Tranberg, J. High Energy Phys. 02 (2016) 107.
  40. M. Postma and G. White, J. High Energy Phys. 03 (2021) 280.
  41. R. Qin and L. Bian, J. High Energy Phys. 08 (2024) 157.
  42. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.111.L051702 for a figure that shows the limitation of the DR with high-temperature expansion at the range Λ∈[590,910]  GeV.
  43. A. Ekstedt, O. Gould, and J. Hirvonen, J. High Energy Phys. 12 (2023) 056.
  44. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D 96, 103520 (2017); 101, 089902(E) (2020).
  45. J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, J. Cosmol. Astropart. Phys. 06 (2010) 028.
  46. A. D. Sakharov, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967).
  47. V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, Phys. Lett. 155B, 36 (1985).
  48. M. E. Shaposhnikov, Nucl. Phys. B287, 757 (1987).
  49. R. Zhou, L. Bian, and H.-K. Guo, Phys. Rev. D 101, 091903 (2020).
  50. X. Gan, A. J. Long, and L.-T. Wang, Phys. Rev. D 96, 115018 (2017).
  51. C. Caprini, R. Durrer, and G. Servant, Phys. Rev. D 77, 124015 (2008).
  52. S. J. Huber and T. Konstandin, J. Cosmol. Astropart. Phys. 09 (2008) 022.
  53. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett. 112, 041301 (2014).
  54. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. D 92, 123009 (2015).
  55. C. Caprini, R. Durrer, and G. Servant, J. Cosmol. Astropart. Phys. 12 (2009) 024.
  56. G. D. Moore and K. Rummukainen, Phys. Rev. D 63, 045002 (2001).
  57. G. D. Moore, K. Rummukainen, and A. Tranberg, J. High Energy Phys. 04 (2001) 017.

Outline

Information

Phys. Rev. D 111, L051702– Published 31 March, 2025
  • Received 20 November 2024
  • Accepted 14 March 2025
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