- 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

Phase diagram of the standard model effective field theory

Mikael Chala*, Maria Cristina Fiore†, and Luis Gil‡

  • *Contact author: mikael.chala@ugr.es
  • †Contact author: mcristinafiore@ugr.es
  • ‡Contact author: lgil@ugr.es
PDF

Phys. Rev. D 113, 115061 – Published 25 June, 2026

DOI: https://doi.org/10.1103/zxzs-d6zt

Abstract

We perform dimensional reduction of the dimension-6 standard model effective field theory (SMEFT) to order g4 in coupling constants g. This analysis includes one-loop contributions to kinetic terms and quartic couplings, as well as two-loop contributions, where operators such as four-fermion interactions first appear, to squared mass terms. Using lattice data, we provide evidence that, in contrast with previous statements in the literature, the SMEFT may undergo a first-order phase transition even for null |ϕ|6 at zero temperature—where ϕ is the Higgs doublet—opening the door to entirely unexplored directions in model building. In such case, however, our analysis implies that the phase transition is not sufficiently strong, narrowing down the new physics that allows for electroweak baryogenesis.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (109)

  1. P. H. Ginsparg, Nucl. Phys. B170, 388 (1980).
  2. T. Appelquist and R. D. Pisarski, Phys. Rev. D 23, 2305 (1981).
  3. T. Matsubara, Prog. Theor. Phys. 14, 351 (1955).
  4. J. Löfgren, J. Phys. G 50, 125008 (2023).
  5. A. D. Linde, Phys. Lett. B 96, 289 (1980).
  6. K. Farakos, K. Kajantie, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B442, 317 (1995).
  7. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B466, 189 (1996).
  8. M. Laine, Nucl. Phys. B451, 484 (1995).
  9. M. Laine and A. Rajantie, Nucl. Phys. B513, 471 (1998).
  10. M. Gurtler, E.-M. Ilgenfritz, and A. Schiller, Phys. Rev. D 56, 3888 (1997).
  11. K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine, and M. E. Shaposhnikov, Nucl. Phys. B532, 283 (1998).
  12. M. Laine and K. Rummukainen, Nucl. Phys. B, Proc. Suppl. 73, 180 (1999).
  13. G. D. Moore and K. Rummukainen, Phys. Rev. D 63, 045002 (2001).
  14. P. B. Arnold and G. D. Moore, Phys. Rev. E 64, 066113 (2001); 68, 049902(E) (2003).
  15. X.-p. Sun, Phys. Rev. E 67, 066702 (2003).
  16. M. D’Onofrio and K. Rummukainen, Phys. Rev. D 93, 025003 (2016).
  17. O. Gould, S. Güyer, and K. Rummukainen, Phys. Rev. D 106, 114507 (2022); 110, 119903(E) (2024).
  18. J. Annala, K. Rummukainen, and T. V. I. Tenkanen, Phys. Rev. D 113, 016014 (2026).
  19. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Nucl. Phys. B458, 90 (1996).
  20. M. Chala and G. Guedes, J. High Energy Phys. 07 (2025) 085.
  21. G. D. Moore, Phys. Rev. D 53, 5906 (1996).
  22. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Phys. Rev. Lett. 77, 2887 (1996).
  23. F. Csikor, Z. Fodor, and J. Heitger, Phys. Rev. Lett. 82, 21 (1999).
  24. G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, Classical Quantum Gravity 23, 4887 (2006); 23, 7361(E) (2006).
  25. S. Kawamura et al., Classical Quantum Gravity 23, S125 (2006).
  26. W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang, Int. J. Mod. Phys. A 35, 2050075 (2020).
  27. J. Aasi et al. (LIGO Scientific Collaboration), Classical Quantum Gravity 32, 074001 (2015).
  28. C. Caprini et al., J. Cosmol. Astropart. Phys. 03 (2020) 024.
  29. T. Brauner, T. V. I. Tenkanen, A. Tranberg, A. Vuorinen, and D. J. Weir, J. High Energy Phys. 03 (2017) 007.
  30. J. O. Andersen, T. Gorda, A. Helset, L. Niemi, T. V. I. Tenkanen, A. Tranberg, A. Vuorinen, and D. J. Weir, Phys. Rev. Lett. 121, 191802 (2018).
  31. L. Niemi, H. H. Patel, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Phys. Rev. D 100, 035002 (2019).
  32. T. Gorda, A. Helset, L. Niemi, T. V. I. Tenkanen, and D. J. Weir, J. High Energy Phys. 02 (2019) 081.
  33. K. Kainulainen, V. Keus, L. Niemi, K. Rummukainen, T. V. I. Tenkanen, and V. Vaskonen, J. High Energy Phys. 06 (2019) 075.
  34. D. Croon, O. Gould, P. Schicho, T. V. I. Tenkanen, and G. White, J. High Energy Phys. 04 (2021) 055.
  35. O. Gould, J. Kozaczuk, L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Phys. Rev. D 100, 115024 (2019).
  36. L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Phys. Rev. Lett. 126, 171802 (2021).
  37. O. Gould and J. Hirvonen, Phys. Rev. D 104, 096015 (2021).
  38. O. Gould, J. High Energy Phys. 04 (2021) 057.
  39. P. M. Schicho, T. V. I. Tenkanen, and J. Österman, J. High Energy Phys. 06 (2021) 130.
  40. L. Niemi, P. Schicho, and T. V. I. Tenkanen, Phys. Rev. D 103, 115035 (2021); 109, 039902(E) (2024).
  41. J. E. Camargo-Molina, R. Enberg, and J. Löfgren, J. High Energy Phys. 10 (2021) 127.
  42. L. Niemi, K. Rummukainen, R. Seppä, and D. J. Weir, J. High Energy Phys. 02 (2023) 212.
  43. A. Ekstedt, Phys. Rev. D 106, 095026 (2022).
  44. A. Ekstedt, O. Gould, and J. Löfgren, Phys. Rev. D 106, 036012 (2022); 110, 019901(E) (2024).
  45. S. Biondini, P. Schicho, and T. V. I. Tenkanen, J. Cosmol. Astropart. Phys. 10 (2022) 044.
  46. P. Schicho, T. V. I. Tenkanen, and G. White, J. High Energy Phys. 11 (2022) 047.
  47. J. Löfgren, M. J. Ramsey-Musolf, P. Schicho, and T. V. I. Tenkanen, Phys. Rev. Lett. 130, 251801 (2023).
  48. O. Gould and C. Xie, J. High Energy Phys. 12 (2023) 049.
  49. M. Kierkla, B. Swiezewska, T. V. I. Tenkanen, and J. van de Vis, J. High Energy Phys. 02 (2024) 234.
  50. G. Aarts et al., Prog. Part. Nucl. Phys. 133, 104070 (2023).
  51. L. Niemi, M. J. Ramsey-Musolf, and G. Xia, Phys. Rev. D 110, 115016 (2024).
  52. M. Chala, J. C. Criado, L. Gil, and J. L. Miras, J. High Energy Phys. 10 (2024) 025.
  53. R. Qin and L. Bian, J. High Energy Phys. 08 (2024) 157.
  54. O. Gould and P. Saffin, J. High Energy Phys. 03 (2025) 105.
  55. J. Chakrabortty and S. Mohanty, Nucl. Phys. B1020, 117165 (2025).
  56. L. Niemi and T. V. I. Tenkanen, Phys. Rev. D 111, 075034 (2025).
  57. M. Kierkla, P. Schicho, B. Swiezewska, T. V. I. Tenkanen, and J. van de Vis, J. High Energy Phys. 07 (2025) 153.
  58. A. Bhatnagar, D. Croon, and P. Schicho, J. High Energy Phys. 03 (2026) 14.
  59. J. López Miras and L. Gil, Proc. Sci. DISCRETE2024 (2025) 089.
  60. F. Bernardo, P. Klose, P. Schicho, and T. V. I. Tenkanen, J. High Energy Phys. 08 (2025) 109.
  61. Y. Zhu, J. Liu, R. Qin, and L. Bian, Phys. Rev. D 112, 015018 (2025).
  62. M. Chala, L. Gil, and Z. Ren, Chin. Phys. 49, 123105 (2025).
  63. X.-X. Li, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and Y. Wu, arXiv:2506.01585.
  64. P. Navarrete, R. Paatelainen, K. Seppänen, and T. V. I. Tenkanen, J. High Energy Phys. 01 (2026) 113.
  65. E. Camargo-Molina, R. Enberg, and J. Löfgren, J. High Energy Phys. 08 (2025) 113.
  66. W. Buchmuller and D. Wyler, Nucl. Phys. B268, 621 (1986).
  67. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, J. High Energy Phys. 10 (2010) 085.
  68. F. P. Huang, P.-H. Gu, P.-F. Yin, Z.-H. Yu, and X. Zhang, Phys. Rev. D 93, 103515 (2016).
  69. T. Huang, J. M. No, L. Pernié, M. Ramsey-Musolf, A. Safonov, M. Spannowsky, and P. Winslow, Phys. Rev. D 96, 035007 (2017).
  70. I. Brivio and M. Trott, Phys. Rep. 793, 1 (2019).
  71. M. J. Ramsey-Musolf, J. High Energy Phys. 09 (2020) 179.
  72. G. Isidori, F. Wilsch, and D. Wyler, Rev. Mod. Phys. 96, 015006 (2024).
  73. J. Aebischer, A. J. Buras, and J. Kumar, arXiv:2507.05926.
  74. O. Gould and T. V. I. Tenkanen, J. High Energy Phys. 01 (2024) 048.
  75. E. Braaten and A. Nieto, Phys. Rev. D 51, 6990 (1995).
  76. T. Hahn, Comput. Phys. Commun. 140, 418 (2001).
  77. V. Shtabovenko, R. Mertig, and F. Orellana, Comput. Phys. Commun. 207, 432 (2016).
  78. E. E. Jenkins, A. V. Manohar, and M. Trott, J. High Energy Phys. 10 (2013) 087.
  79. E. E. Jenkins, A. V. Manohar, and M. Trott, J. High Energy Phys. 01 (2014) 035.
  80. R. Alonso, E. E. Jenkins, A. V. Manohar, and M. Trott, J. High Energy Phys. 04 (2014) 159.
  81. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zxzs-d6zt for matching relations in Wolfram language.
  82. J. Ellis, M. Madigan, K. Mimasu, V. Sanz, and T. You, J. High Energy Phys. 04 (2021) 279.
  83. J. J. Ethier, G. Magni, F. Maltoni, L. Mantani, E. R. Nocera, J. Rojo, E. Slade, E. Vryonidou, and C. Zhang (SMEFiT Collaboration), J. High Energy Phys. 11 (2021) 089.
  84. J. de Blas, A. Goncalves, V. Miralles, L. Reina, L. Silvestrini, and M. Valli, J. High Energy Phys. 03 (2026) 013.
  85. T. Giani, G. Magni, and J. Rojo, Eur. Phys. J. C 83, 393 (2023).
  86. M. Postma and G. White, J. High Energy Phys. 03 (2021) 280.
  87. X.-m. Zhang, Phys. Rev. D 47, 3065 (1993).
  88. D. Bodeker, L. Fromme, S. J. Huber, and M. Seniuch, J. High Energy Phys. 02 (2005) 026.
  89. C. Grojean, G. Servant, and J. D. Wells, Phys. Rev. D 71, 036001 (2005).
  90. S. W. Ham and S. K. Oh, Phys. Rev. D 70, 093007 (2004).
  91. C. Delaunay, C. Grojean, and J. D. Wells, J. High Energy Phys. 04 (2008) 029.
  92. B. Grinstein and M. Trott, Phys. Rev. D 78, 075022 (2008).
  93. P. H. Damgaard, A. Haarr, D. O’Connell, and A. Tranberg, J. High Energy Phys. 02 (2016) 107.
  94. J. de Vries, M. Postma, J. van de Vis, and G. White, J. High Energy Phys. 01 (2018) 089.
  95. R.-G. Cai, M. Sasaki, and S.-J. Wang, J. Cosmol. Astropart. Phys. 08 (2017) 004.
  96. M. Chala, C. Krause, and G. Nardini, J. High Energy Phys. 07 (2018) 062.
  97. J. Ellis, M. Lewicki, and J. M. No, J. Cosmol. Astropart. Phys. 04 (2019) 003.
  98. J. Ellis, M. Lewicki, J. M. No, and V. Vaskonen, J. Cosmol. Astropart. Phys. 06 (2019) 024.
  99. J. Ellis, M. Fairbairn, M. Lewicki, V. Vaskonen, and A. Wickens, J. Cosmol. Astropart. Phys. 09 (2019) 019.
  100. V. Q. Phong, P. H. Khiem, N. P. D. Loc, and H. N. Long, Phys. Rev. D 101, 116010 (2020).
  101. K. Hashino and D. Ueda, Phys. Rev. D 107, 095022 (2023).
  102. S. Kanemura, R. Nagai, and M. Tanaka, J. High Energy Phys. 06 (2022) 027.
  103. R. Alonso, J. C. Criado, R. Houtz, and M. West, J. High Energy Phys. 05 (2024) 049.
  104. V. K. Oikonomou and A. Giovanakis, Phys. Rev. D 109, 055044 (2024).
  105. K. Hashino and D. Ueda, J. High Energy Phys. 09 (2025) 094.
  106. J. M. No and M. Ramsey-Musolf, Phys. Rev. D 89, 095031 (2014).
  107. H.-L. Li, M. Ramsey-Musolf, and S. Willocq, Phys. Rev. D 100, 075035 (2019).
  108. P. Basler, S. Dawson, C. Englert, and M. Mühlleitner, Phys. Rev. D 101, 015019 (2020).
  109. L. Biermann, C. Borschensky, C. Englert, M. Mühlleitner, and W. Naskar, Phys. Rev. D 110, 095012 (2024).

Outline

Information

Phys. Rev. D 113, 115061– Published 25 June, 2026
  • Received 30 July 2025
  • Accepted 20 April 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