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Multistep strong first-order electroweak phase transitions in the inverted type-I 2HDM: Parameter space, gravitational waves, and collider phenomenology

Soojin Lee1,*, Dongjoo Kim1,†, Jin-Hwan Cho2,‡, Jinheung Kim3,§, and Jeonghyeon Song1,∥

  • *Contact author: soojinlee957@gmail.com
  • †Contact author: dongjookim.phys@gmail.com
  • ‡Contact author: chof@nims.re.kr
  • §Contact author: jhkim1216@kias.re.kr
  • ∥Contact author: jhsong@konkuk.ac.kr
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Phys. Rev. D 112, 055035 – Published 24 September, 2025

DOI: https://doi.org/10.1103/cbgr-w9cb

Abstract

We investigate the electroweak phase transition (EWPT) within the inverted type-I two-Higgs-doublet model, where the observed 125 GeV Higgs boson is identified as the heavier CP-even scalar H. Through a comprehensive parameter-space scan consistent with current theoretical and experimental constraints, we identify regions supporting strong first-order EWPTs (SFOEWPTs), including multistep transitions. We find that two-step SFOEWPTs occur as frequently as one-step transitions, while three-step transitions can occur, albeit rarely. Crucially, the parameter spaces inducing one-step and two-step transitions are partially yet significantly separated: one-step transitions restrict the charged Higgs mass and tanβ to mH±∈[295,441]  GeV and tanβ∈[4.2,8.8], whereas two-step transitions allow mH±∈[100,350]  GeV and tanβ∈[2.5,45.4]. Notably, negative values of sin(β−α) arise almost exclusively in one-step scenarios. We present the calculation of gravitational wave (GW) signal-to-noise ratios (SNRs) at Laser Interferometer Space Antenna for multistep EWPTs, finding that detectable GW signals (SNR>10) predominantly emerge from two-step transitions. Furthermore, we demonstrate that the previously established correlation between the vacuum uplifting measure ΔF0 and EWPT strength ξc persists only in one-step transitions and breaks down in multistep cases. Finally, we perform a dedicated collider analysis for representative SFOEWPT parameter points at the 1.5 TeV Compact Linear Collider, identifying e+e−→H+H−→W+W−hh as a promising discovery channel. Enhanced h→γγ branching ratios for negative sin(β−α) motivate two complementary golden final states, W+W−bb¯τ+τ− and W+W−bb¯γγ, which demonstrate high discovery potential due to negligible Standard Model backgrounds.

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References (205)

  1. P. A. R. Ade et al. (Planck Collaboration), Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594, A13 (2016).
  2. A. D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967).
  3. P. Huet and E. Sather, Electroweak baryogenesis and standard model CP violation, Phys. Rev. D 51, 379 (1995).
  4. K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov, Is there a hot electroweak phase transition at mH≳mW?, Phys. Rev. Lett. 77, 2887 (1996).
  5. F. Csikor, Z. Fodor, and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. Rev. Lett. 82, 21 (1999).
  6. M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71, 1463 (1999).
  7. A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Progress in electroweak baryogenesis, Annu. Rev. Nucl. Part. Sci. 43, 27 (1993).
  8. M. Carena, M. Quiros, and C. E. M. Wagner, Opening the window for electroweak baryogenesis, Phys. Lett. B 380, 81 (1996).
  9. D. E. Morrissey and M. J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14, 125003 (2012).
  10. D. J. Weir, Gravitational waves from a first order electroweak phase transition: A brief review, Phil. Trans. R. Soc. A 376, 20170126 (2018); 381, 20230212(E) (2023).
  11. C. Caprini and D. G. Figueroa, Cosmological backgrounds of gravitational waves, Classical Quantum Gravity 35, 163001 (2018).
  12. P. Amaro-Seoane et al. (LISA Collaboration), Laser interferometer space antenna, arXiv:1702.00786.
  13. D. Cutting, M. Hindmarsh, and D. J. Weir, Gravitational waves from vacuum first-order phase transitions: From the envelope to the lattice, Phys. Rev. D 97, 123513 (2018).
  14. H.-K. Guo, K. Sinha, D. Vagie, and G. White, Phase transitions in an expanding universe: Stochastic gravitational waves in standard and non-standard histories, J. Cosmol. Astropart. Phys. 01 (2021) 001.
  15. K. Schmitz, New sensitivity curves for gravitational-wave signals from cosmological phase transitions, J. High Energy Phys. 01 (2021) 097.
  16. M. Carena, Z. Liu, and M. Riembau, Probing the electroweak phase transition via enhanced di-Higgs boson production, Phys. Rev. D 97, 095032 (2018).
  17. J. M. Cline and K. Kainulainen, Electroweak baryogenesis and dark matter from a singlet Higgs, J. Cosmol. Astropart. Phys. 01 (2013) 012.
  18. J. M. Cline, K. Kainulainen, and D. Tucker-Smith, Electroweak baryogenesis from a dark sector, Phys. Rev. D 95, 115006 (2017).
  19. M. Carena, M. Quirós, and Y. Zhang, Electroweak baryogenesis from dark-sector CP violation, Phys. Rev. Lett. 122, 201802 (2019).
  20. J. M. Cline, G. Laporte, H. Yamashita, and S. Kraml, Electroweak phase transition and LHC signatures in the singlet Majoron model, J. High Energy Phys. 07 (2009) 040.
  21. S. Profumo, M. J. Ramsey-Musolf, C. L. Wainwright, and P. Winslow, Singlet-catalyzed electroweak phase transitions and precision Higgs boson studies, Phys. Rev. D 91, 035018 (2015).
  22. D. Curtin, P. Meade, and C.-T. Yu, Testing electroweak baryogenesis with future colliders, J. High Energy Phys. 11 (2014) 127.
  23. F. P. Huang and C. S. Li, Electroweak baryogenesis in the framework of the effective field theory, Phys. Rev. D 92, 075014 (2015).
  24. A. V. Kotwal, M. J. Ramsey-Musolf, J. M. No, and P. Winslow, Singlet-catalyzed electroweak phase transitions in the 100 TeV frontier, Phys. Rev. D 94, 035022 (2016).
  25. V. Vaskonen, Electroweak baryogenesis and gravitational waves from a real scalar singlet, Phys. Rev. D 95, 123515 (2017).
  26. A. Beniwal, M. Lewicki, J. D. Wells, M. White, and A. G. Williams, Gravitational wave, collider and dark matter signals from a scalar singlet electroweak baryogenesis, J. High Energy Phys. 08 (2017) 108.
  27. G. Kurup and M. Perelstein, Dynamics of electroweak phase transition in singlet-scalar extension of the Standard Model, Phys. Rev. D 96, 015036 (2017).
  28. C.-W. Chiang, M. J. Ramsey-Musolf, and E. Senaha, Standard model with a complex scalar singlet: Cosmological implications and theoretical considerations, Phys. Rev. D 97, 015005 (2018).
  29. A. Alves, T. Ghosh, H.-K. Guo, K. Sinha, and D. Vagie, Collider and gravitational wave complementarity in exploring the singlet extension of the standard model, J. High Energy Phys. 04 (2019) 052.
  30. H.-L. Li, M. Ramsey-Musolf, and S. Willocq, Probing a scalar singlet-catalyzed electroweak phase transition with resonant di-Higgs boson production in the 4b channel, Phys. Rev. D 100, 075035 (2019).
  31. N. F. Bell, M. J. Dolan, L. S. Friedrich, M. J. Ramsey-Musolf, and R. R. Volkas, Electroweak baryogenesis with vector-like leptons and scalar singlets, J. High Energy Phys. 09 (2019) 012.
  32. B. Grzadkowski and D. Huang, Spontaneous CP-violating electroweak baryogenesis and dark matter from a complex singlet scalar, J. High Energy Phys. 08 (2018) 135.
  33. F. P. Huang, Z. Qian, and M. Zhang, Exploring dynamical CP violation induced baryogenesis by gravitational waves and colliders, Phys. Rev. D 98, 015014 (2018).
  34. P. Ghosh, T. Ghosh, and S. Roy, Interplay among gravitational waves, dark matter and collider signals in the singlet scalar extended type-II seesaw model, J. High Energy Phys. 10 (2023) 057.
  35. S. Roy, Dilution of dark matter relic abundance due to first order electroweak phase transition in the singlet scalar extended type-II seesaw model, Phys. Rev. D 111, 015037 (2025).
  36. A. Azatov, G. Barni, S. Chakraborty, M. Vanvlasselaer, and W. Yin, Ultra-relativistic bubbles from the simplest Higgs portal and their cosmological consequences, J. High Energy Phys. 10 (2022) 017.
  37. S. Inoue, G. Ovanesyan, and M. J. Ramsey-Musolf, Two-step electroweak baryogenesis, Phys. Rev. D 93, 015013 (2016).
  38. L. Niemi, H. H. Patel, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Electroweak phase transition in the real triplet extension of the SM: Dimensional reduction, Phys. Rev. D 100, 035002 (2019).
  39. M. Chala, M. Ramos, and M. Spannowsky, Gravitational wave and collider probes of a triplet Higgs sector with a low cutoff, Eur. Phys. J. C 79, 156 (2019).
  40. R. Zhou, W. Cheng, X. Deng, L. Bian, and Y. Wu, Electroweak phase transition and Higgs phenomenology in the Georgi-Machacek model, J. High Energy Phys. 01 (2019) 216.
  41. M. J. Kazemi and S. S. Abdussalam, Electroweak phase transition in an inert complex triplet model, Phys. Rev. D 103, 075012 (2021).
  42. A. Addazi, A. Marciano, A. P. Morais, R. Pasechnik, and H. Yang, CDF II W-mass anomaly faces first-order electroweak phase transition, Eur. Phys. J. C 83, 207 (2023).
  43. A. Crivellin, S. Ashanujjaman, S. Banik, G. Coloretti, S. P. Maharathy, and B. Mellado, Growing evidence for a Higgs triplet*, Chin. Phys. C 49, 053107 (2025).
  44. P. Borah, P. Ghosh, and A. K. Saha, Prospecting bipartite dark matter through gravitational waves, J. Cosmol. Astropart. Phys. 05 (2025) 035.
  45. C.-T. Lu, Y. Wu, and S. Xu, Dark matter and electroweak phase transition in the Z2 symmetric Georgi-Machacek model, arXiv:2504.10930.
  46. P. Borah and P. Ghosh, Unveiling the inert triplet desert region with a pNGB dark matter and its gravitational wave signatures, arXiv:2505.16521.
  47. J. M. Cline, M. Jarvinen, and F. Sannino, The electroweak phase transition in nearly conformal technicolor, Phys. Rev. D 78, 075027 (2008).
  48. L. Bian, Y. Wu, and K.-P. Xie, Electroweak phase transition with composite Higgs models: Calculability, gravitational waves and collider searches, J. High Energy Phys. 12 (2019) 028.
  49. K.-P. Xie, L. Bian, and Y. Wu, Electroweak baryogenesis and gravitational waves in a composite Higgs model with high dimensional fermion representations, J. High Energy Phys. 12 (2020) 047.
  50. J. M. Cline, M. Joyce, and K. Kainulainen, Supersymmetric electroweak baryogenesis in the WKB approximation, Phys. Lett. B 417, 79 (1998); 448, 321(E) (1999).
  51. A. Menon, D. E. Morrissey, and C. E. M. Wagner, Electroweak baryogenesis and dark matter in the nMSSM, Phys. Rev. D 70, 035005 (2004).
  52. M. Carena, N. R. Shah, and C. E. M. Wagner, Light dark matter and the electroweak phase transition in the NMSSM, Phys. Rev. D 85, 036003 (2012).
  53. X.-J. Bi, L. Bian, W. Huang, J. Shu, and P.-F. Yin, Interpretation of the Galactic Center excess and electroweak phase transition in the NMSSM, Phys. Rev. D 92, 023507 (2015).
  54. S. V. Demidov, D. S. Gorbunov, and D. V. Kirpichnikov, Split NMSSM with electroweak baryogenesis, J. High Energy Phys. 11 (2016) 148.
  55. W. Huang, Z. Kang, J. Shu, P. Wu, and J. M. Yang, New insights in the electroweak phase transition in the NMSSM, Phys. Rev. D 91, 025006 (2015).
  56. K. Cheung, T.-J. Hou, J. S. Lee, and E. Senaha, Singlino-driven electroweak baryogenesis in the next-to-MSSM, Phys. Lett. B 710, 188 (2012).
  57. C. Balázs, A. Mazumdar, E. Pukartas, and G. White, Baryogenesis, dark matter and inflation in the next-to-minimal supersymmetric standard model, J. High Energy Phys. 01 (2014) 073.
  58. S. J. Huber, T. Konstandin, T. Prokopec, and M. G. Schmidt, Electroweak phase transition and baryogenesis in the nMSSM, Nucl. Phys. B757, 172 (2006).
  59. L. Bian, H.-K. Guo, and J. Shu, Gravitational waves, baryon asymmetry of the universe and electric dipole moment in the CP-violating NMSSM, Chin. Phys. C 42, 093106 (2018); 43, 129101(E) (2019).
  60. J. Kozaczuk, S. Profumo, L. S. Haskins, and C. L. Wainwright, Cosmological phase transitions and their properties in the NMSSM, J. High Energy Phys. 01 (2015) 144.
  61. A. Katz, M. Perelstein, M. J. Ramsey-Musolf, and P. Winslow, Stop-catalyzed baryogenesis beyond the MSSM, Phys. Rev. D 92, 095019 (2015).
  62. S. Akula, C. Balázs, L. Dunn, and G. White, Electroweak baryogenesis in the Z3-invariant NMSSM, J. High Energy Phys. 11 (2017) 051.
  63. C. Lee, V. Cirigliano, and M. J. Ramsey-Musolf, Resonant relaxation in electroweak baryogenesis, Phys. Rev. D 71, 075010 (2005).
  64. C. Balazs, M. Carena, A. Menon, D. E. Morrissey, and C. E. M. Wagner, The supersymmetric origin of matter, Phys. Rev. D 71, 075002 (2005).
  65. S. Liebler, S. Profumo, and T. Stefaniak, Light stop mass limits from Higgs rate measurements in the MSSM: Is MSSM electroweak baryogenesis still alive after all?, J. High Energy Phys. 04 (2016) 143.
  66. A. Chatterjee, A. Datta, and S. Roy, Electroweak phase transition in the Z3-invariant NMSSM: Implications of LHC and dark matter searches and prospects of detecting the gravitational waves, J. High Energy Phys. 06 (2022) 108.
  67. P. Borah, P. Ghosh, S. Roy, and A. K. Saha, Electroweak phase transition in a right-handed neutrino superfield extended NMSSM, J. High Energy Phys. 08 (2023) 029.
  68. A. Kobakhidze, L. Wu, and J. Yue, Electroweak baryogenesis with anomalous Higgs couplings, J. High Energy Phys. 04 (2016) 011.
  69. M. J. Ramsey-Musolf, P. Winslow, and G. White, Color breaking baryogenesis, Phys. Rev. D 97, 123509 (2018).
  70. S. Yaser Ayazi and A. Mohamadnejad, Conformal vector dark matter and strongly first-order electroweak phase transition, J. High Energy Phys. 03 (2019) 181.
  71. A. Mohamadnejad, Gravitational waves from scale-invariant vector dark matter model: Probing below the neutrino-floor, Eur. Phys. J. C 80, 197 (2020).
  72. A. I. Bochkarev, S. V. Kuzmin, and M. E. Shaposhnikov, Electroweak baryogenesis and the Higgs boson mass problem, Phys. Lett. B 244, 275 (1990).
  73. G. C. Dorsch, S. J. Huber, and J. M. No, A strong electroweak phase transition in the 2HDM after LHC8, J. High Energy Phys. 10 (2013) 029.
  74. P. Basler, M. Krause, M. Muhlleitner, J. Wittbrodt, and A. Wlotzka, Strong first order electroweak phase transition in the CP-conserving 2HDM revisited, J. High Energy Phys. 02 (2017) 121.
  75. K. Fuyuto, W.-S. Hou, and E. Senaha, Electroweak baryogenesis driven by extra top Yukawa couplings, Phys. Lett. B 776, 402 (2018).
  76. J. Bernon, L. Bian, and Y. Jiang, A new insight into the phase transition in the early Universe with two Higgs doublets, J. High Energy Phys. 05 (2018) 151.
  77. K. Kainulainen, V. Keus, L. Niemi, K. Rummukainen, T. V. I. Tenkanen, and V. Vaskonen, On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model, J. High Energy Phys. 06 (2019) 075.
  78. P. Bittar, S. Roy, and C. E. M. Wagner, Self consistent thermal resummation: A case study of the phase transition in 2HDM, arXiv:2504.02024.
  79. G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rep. 516, 1 (2012).
  80. S. L. Glashow and S. Weinberg, Natural conservation laws for neutral currents, Phys. Rev. D 15, 1958 (1977).
  81. E. A. Paschos, Diagonal neutral currents, Phys. Rev. D 15, 1966 (1977).
  82. H. E. Haber and Y. Nir, Multiscalar models with a high-energy scale, Nucl. Phys. B335, 363 (1990).
  83. H. E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model. II. The significance of tanβ, Phys. Rev. D 74, 015018 (2006); 74, 059905(E) (2006).
  84. D. M. Asner et al., ILC Higgs white paper, arXiv:1310.0763.
  85. J. F. Gunion and H. E. Haber, The CP conserving two Higgs doublet model: He approach to the decoupling limit, Phys. Rev. D 67, 075019 (2003).
  86. M. Quiros, Finite temperature field theory and phase transitions, in ICTP Summer School in High-Energy Physics and Cosmology (1999), pp. 187–259, .
  87. L. Niemi, P. Schicho, and T. V. I. Tenkanen, Singlet-assisted electroweak phase transition at two loops, Phys. Rev. D 103, 115035 (2021); 109, 039902(E) (2024).
  88. H. Bahl, M. Carena, A. Ireland, and C. E. M. Wagner, Improved thermal resummation for multi-field potentials, J. High Energy Phys. 09 (2024) 153.
  89. I. Masina and M. Quiros, An introduction to effective potential methods in field theory, arXiv:2501.12713.
  90. W. Su, A. G. Williams, and M. Zhang, Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories, J. High Energy Phys. 04 (2021) 219.
  91. J. Haller, A. Hoecker, R. Kogler, K. Mönig, T. Peiffer, and J. Stelzer, Update of the global electroweak fit and constraints on two-Higgs-doublet models, Eur. Phys. J. C 78, 675 (2018).
  92. M. Misiak, A. Rehman, and M. Steinhauser, Towards B¯→Xsγ at the NNLO in QCD without interpolation in mc, J. High Energy Phys. 06 (2020) 175.
  93. T. Biekötter, D. Fontes, M. Mühlleitner, J. C. Romão, R. Santos, and J. P. Silva, Impact of new experimental data on the C2HDM: The strong interdependence between LHC Higgs data and the electron EDM, J. High Energy Phys. 05 (2024) 127.
  94. T. Biekötter and M. O. Olea-Romacho, Benchmarking a fading window: Electroweak baryogenesis in the C2HDM, LHC constraints after Run 2 and prospects for LISA, arXiv:2505.09670.
  95. M. Aoki, T. Komatsu, and H. Shibuya, Possibility of a multi-step electroweak phase transition in the two-Higgs doublet models, Prog. Theor. Exp. Phys. 2022, 063B05 (2022).
  96. D. Gonçalves, A. Kaladharan, and Y. Wu, Electroweak phase transition in the 2HDM: Collider and gravitational wave complementarity, Phys. Rev. D 105, 095041 (2022).
  97. Z. Si, H. Wang, L. Wang, and Y. Zhang, Exploring multi-step electroweak phase transitions in the 2HDM+a, Eur. Phys. J. C 85, 273 (2025).
  98. D. Land and E. D. Carlson, Two stage phase transition in two Higgs models, Phys. Lett. B 292, 107 (1992).
  99. H. H. Patel and M. J. Ramsey-Musolf, Stepping into electroweak symmetry breaking: Phase transitions and Higgs phenomenology, Phys. Rev. D 88, 035013 (2013).
  100. N. Blinov, J. Kozaczuk, D. E. Morrissey, and C. Tamarit, Electroweak baryogenesis from exotic electroweak symmetry breaking, Phys. Rev. D 92, 035012 (2015).
  101. W. Chao, H.-K. Guo, and J. Shu, Gravitational wave signals of electroweak phase transition triggered by dark matter, J. Cosmol. Astropart. Phys. 09 (2017) 009.
  102. A. P. Morais and R. Pasechnik, Probing multi-step electroweak phase transition with multi-peaked primordial gravitational waves spectra, J. Cosmol. Astropart. Phys. 04 (2020) 036.
  103. S. Fabian, F. Goertz, and Y. Jiang, Dark matter and nature of electroweak phase transition with an inert doublet, J. Cosmol. Astropart. Phys. 09 (2021) 011.
  104. A. Angelescu and P. Huang, Multistep strongly first order phase transitions from new fermions at the TeV scale, Phys. Rev. D 99, 055023 (2019).
  105. L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir, Thermodynamics of a two-step electroweak phase transition, Phys. Rev. Lett. 126, 171802 (2021).
  106. G. C. Dorsch, S. J. Huber, K. Mimasu, and J. M. No, The Higgs vacuum uplifted: Revisiting the electroweak phase transition with a second Higgs doublet, J. High Energy Phys. 12 (2017) 086.
  107. J. Song and Y. W. Yoon, Wγ decay of the elusive charged Higgs boson in the two-Higgs-doublet model with vectorlike fermions, Phys. Rev. D 100, 055006 (2019).
  108. S. Chang, S. K. Kang, J.-P. Lee, and J. Song, Higgs potential and hidden light Higgs scenario in two Higgs doublet models, Phys. Rev. D 92, 075023 (2015).
  109. A. Jueid, J. Kim, S. Lee, and J. Song, Type-X two-Higgs-doublet model in light of the muon g-2: Confronting Higgs boson and collider data, Phys. Rev. D 104, 095008 (2021).
  110. K. Cheung, A. Jueid, J. Kim, S. Lee, C.-T. Lu, and J. Song, Comprehensive study of the light charged Higgs boson in the type-I two-Higgs-doublet model, Phys. Rev. D 105, 095044 (2022).
  111. S. Lee, K. Cheung, J. Kim, C.-T. Lu, and J. Song, Status of the two-Higgs-doublet model in light of the CDF mW measurement, Phys. Rev. D 106, 075013 (2022).
  112. J. R. Espinosa, M. Quiros, and F. Zwirner, On the nature of the electroweak phase transition, Phys. Lett. B 314, 206 (1993).
  113. N. Herring, S. Cao, and D. Boyanovsky, Is the finite temperature effective potential effective for dynamics?, Phys. Rev. D 111, 016028 (2025).
  114. J. Chakrabortty and S. Mohanty, One loop thermal effective action, arXiv:2411.14146.
  115. P. M. Ferreira and B. Swiezewska, One-loop contributions to neutral minima in the inert doublet model, J. High Energy Phys. 04 (2016) 099.
  116. S. R. Coleman and E. J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7, 1888 (1973).
  117. L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9, 3320 (1974).
  118. M. E. Carrington, The effective potential at finite temperature in the Standard Model, Phys. Rev. D 45, 2933 (1992).
  119. P. B. Arnold and O. Espinosa, The effective potential and first order phase transitions: Beyond leading-order, Phys. Rev. D 47, 3546 (1993); 50, 6662(E) (1994).
  120. S. R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15, 2929 (1977); 16, 1248(E) (1977).
  121. A. D. Linde, Fate of the false vacuum at finite temperature: Theory and applications, Phys. Lett. 100B, 37 (1981).
  122. C. P. D. Harman and S. J. Huber, Does zero temperature decide on the nature of the electroweak phase transition?, J. High Energy Phys. 06 (2016) 005.
  123. T. V. I. Tenkanen and J. van de Vis, Speed of sound in cosmological phase transitions and effect on gravitational waves, J. High Energy Phys. 08 (2022) 302.
  124. R. Caldwell et al., Detection of early-universe gravitational-wave signatures and fundamental physics, Gen. Relativ. Gravit. 54, 156 (2022).
  125. P. Auclair et al. (LISA Cosmology Working Group Collaboration), Cosmology with the laser interferometer space antenna, Living Rev. Relativity 26, 5 (2023).
  126. C. Caprini, M. Chala, G. C. Dorsch, M. Hindmarsh, S. J. Huber, T. Konstandin, J. Kozaczuk, G. Nardini, J. M. No, K. Rummukainen et al., Detecting gravitational waves from cosmological phase transitions with LISA: An update, J. Cosmol. Astropart. Phys. 03 (2020) 024.
  127. P. Basler, L. Biermann, M. Mühlleitner, J. Müller, R. Santos, and J. Viana, bsmpt v3 A tool for phase transitions and primordial gravitational waves in extended Higgs sectors, Comput. Phys. Commun. 316, 109766 (2025).
  128. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition, Phys. Rev. D 92, 123009 (2015).
  129. M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Shape of the acoustic gravitational wave power spectrum from a first order phase transition, Phys. Rev. D 96, 103520 (2017); 101, 089902(E) (2020).
  130. C. Grojean and G. Servant, Gravitational waves from phase transitions at the electroweak scale and beyond, Phys. Rev. D 75, 043507 (2007).
  131. L. Leitao and A. Megevand, Gravitational waves from a very strong electroweak phase transition, J. Cosmol. Astropart. Phys. 05 (2016) 037.
  132. C. Caprini, M. Hindmarsh, S. Huber, T. Konstandin, J. Kozaczuk, G. Nardini, J. M. No, A. Petiteau, P. Schwaller, G. Servant et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, J. Cosmol. Astropart. Phys. 04 (2016) 001.
  133. J. Ellis, M. Lewicki, and J. M. No, On the maximal strength of a first-order electroweak phase transition and its gravitational wave signal, J. Cosmol. Astropart. Phys. 04 (2019) 003.
  134. W.-Y. Ai, B. Garbrecht, and C. Tamarit, Bubble wall velocities in local equilibrium, J. Cosmol. Astropart. Phys. 03 (2022) 015.
  135. G. C. Dorsch, S. J. Huber, and T. Konstandin, A sonic boom in bubble wall friction, J. Cosmol. Astropart. Phys. 04 (2022) 010.
  136. S. Jiang, F. P. Huang, and X. Wang, Bubble wall velocity during electroweak phase transition in the inert doublet model, Phys. Rev. D 107, 095005 (2023).
  137. S. De Curtis, L. D. Rose, A. Guiggiani, A. G. Muyor, and G. Panico, Bubble wall dynamics at the electroweak phase transition, J. High Energy Phys. 03 (2022) 163.
  138. W.-Y. Ai, B. Laurent, and J. van de Vis, Model-independent bubble wall velocities in local thermal equilibrium, J. Cosmol. Astropart. Phys. 07 (2023) 002.
  139. S. De Curtis, L. Delle Rose, A. Guiggiani, A. Gil Muyor, and G. Panico, Collision integrals for cosmological phase transitions, J. High Energy Phys. 05 (2023) 194.
  140. T. Krajewski, M. Lewicki, and M. Zych, Bubble-wall velocity in local thermal equilibrium: Hydrodynamical simulations vs analytical treatment, J. High Energy Phys. 05 (2024) 011.
  141. D.-W. Wang, Q.-S. Yan, and M. Huang, Bubble wall velocity and gravitational wave in the minimal left-right symmetric model, Phys. Rev. D 110, 076011 (2024).
  142. S. De Curtis, L. Delle Rose, A. Guiggiani, A. Gil Muyor, and G. Panico, Non-linearities in cosmological bubble wall dynamics, J. High Energy Phys. 05 (2024) 009.
  143. C. Branchina, A. Conaci, S. De Curtis, and L. Delle Rose, Electroweak phase transition and bubble wall velocity in local thermal equilibrium, arXiv:2504.21213.
  144. M. Lewicki, M. Merchand, and M. Zych, Electroweak bubble wall expansion: Gravitational waves and baryogenesis in standard model-like thermal plasma, J. High Energy Phys. 02 (2022) 017.
  145. B. Laurent and J. M. Cline, First principles determination of bubble wall velocity, Phys. Rev. D 106, 023501 (2022).
  146. T. Biekötter, S. Heinemeyer, J. M. No, M. O. Olea-Romacho, and G. Weiglein, The trap in the early Universe: Impact on the interplay between gravitational waves and LHC physics in the 2HDM, J. Cosmol. Astropart. Phys. 03 (2023) 031.
  147. M. J. Ramsey-Musolf, V. Q. Tran, and T.-C. Yuan, Gravitational waves and dark matter in the gauged two-Higgs doublet model, J. High Energy Phys. 01 (2025) 129.
  148. C. Caprini and R. Durrer, Gravitational wave production: A strong constraint on primordial magnetic fields, Phys. Rev. D 65, 023517 (2001).
  149. D. G. Figueroa, M. Hindmarsh, and J. Urrestilla, Exact scale-invariant background of gravitational waves from cosmic defects, Phys. Rev. Lett. 110, 101302 (2013).
  150. M. Hindmarsh, Sound shell model for acoustic gravitational wave production at a first-order phase transition in the early Universe, Phys. Rev. Lett. 120, 071301 (2018).
  151. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  152. P. Athron, C. Balázs, A. Fowlie, L. Morris, and L. Wu, Cosmological phase transitions: From perturbative particle physics to gravitational waves, Prog. Part. Nucl. Phys. 135, 104094 (2024).
  153. P. Athron, C. Balázs, A. Fowlie, and Y. Zhang, phasetracer: Tracing cosmological phases and calculating transition properties, Eur. Phys. J. C 80, 567 (2020).
  154. J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant, Energy budget of cosmological first-order phase transitions, J. Cosmol. Astropart. Phys. 06 (2010) 028.
  155. P. J. Steinhardt, Relativistic detonation waves and bubble growth in false vacuum decay, Phys. Rev. D 25, 2074 (1982).
  156. M. Kamionkowski, A. Kosowsky, and M. S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49, 2837 (1994).
  157. C. Caprini, D. G. Figueroa, R. Flauger, G. Nardini, M. Peloso, M. Pieroni, A. Ricciardone, and G. Tasinato, Reconstructing the spectral shape of a stochastic gravitational wave background with LISA, J. Cosmol. Astropart. Phys. 11 (2019) 017.
  158. S. Babak, A. Petiteau, and M. Hewitson, LISA sensitivity and SNR calculations, arXiv:2108.01167.
  159. A. Barroso, P. M. Ferreira, I. P. Ivanov, and R. Santos, Metastability bounds on the two Higgs doublet model, J. High Energy Phys. 06 (2013) 045.
  160. I. P. Ivanov and J. P. Silva, Tree-level metastability bounds for the most general two Higgs doublet model, Phys. Rev. D 92, 055017 (2015).
  161. I. P. Ivanov, General two-order-parameter Ginzburg-Landau model with quadratic and quartic interactions, Phys. Rev. E 79, 021116 (2009).
  162. A. Barroso, P. M. Ferreira, I. P. Ivanov, R. Santos, and J. P. Silva, Evading death by vacuum, Eur. Phys. J. C 73, 2537 (2013).
  163. I. P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM, Phys. Rev. D 75, 035001 (2007); 76, 039902(E) (2007).
  164. A. Arhrib, Unitarity constraints on scalar parameters of the standard and two Higgs doublets model, in Proceedings of the Workshop on Noncommutative Geometry, Superstrings and Particle Physics (2000), arXiv:hep-ph/0012353.
  165. M. E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46, 381 (1992).
  166. H.-J. He, N. Polonsky, and S.-f. Su, Extra families, Higgs spectrum and oblique corrections, Phys. Rev. D 64, 053004 (2001).
  167. W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, The Oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B801, 81 (2008).
  168. A. Arbey, F. Mahmoudi, O. Stal, and T. Stefaniak, Status of the charged Higgs boson in two Higgs doublet models, Eur. Phys. J. C 78, 182 (2018).
  169. P. Sanyal, Limits on the charged Higgs parameters in the two Higgs doublet model using CMS s=13  TeV results, Eur. Phys. J. C 79, 913 (2019).
  170. M. Misiak and M. Steinhauser, Weak radiative decays of the B meson and bounds on MH± in the two-Higgs-doublet model, Eur. Phys. J. C 77, 201 (2017).
  171. T. Horiguchi et al. (Belle Collaboration), Evidence for isospin violation and measurement of CP asymmetries in B→K*(892)γ, Phys. Rev. Lett. 119, 191802 (2017).
  172. D. Dutta et al. (Belle Collaboration), Search for Bs0→γγ and a measurement of the branching fraction for Bs0→ϕγ, Phys. Rev. D 91, 011101 (2015).
  173. D. Eriksson, J. Rathsman, and O. Stal, 2HDMC: Two-Higgs-doublet model calculator physics and manual, Comput. Phys. Commun. 181, 189 (2010).
  174. M. Mühlleitner, M. O. P. Sampaio, R. Santos, and J. Wittbrodt, ScannerS: Parameter scans in extended scalar sectors, Eur. Phys. J. C 82, 198 (2022).
  175. H. Bahl, T. Biekötter, S. Heinemeyer, C. Li, S. Paasch, G. Weiglein, and J. Wittbrodt, higgstools: BSM scalar phenomenology with new versions of HiggsBounds and HiggsSignals, Comput. Phys. Commun. 291, 108803 (2023).
  176. C. L. Wainwright, cosmotransitions: Computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183, 2006 (2012).
  177. P. Basler and M. Mühlleitner, BSMPT (Beyond the Standard Model Phase Transitions): A tool for the electroweak phase transition in extended Higgs sectors, Comput. Phys. Commun. 237, 62 (2019).
  178. P. Basler, M. Mühlleitner, and J. Müller, BSMPT v2 a tool for the electroweak phase transition and the baryon asymmetry of the universe in extended Higgs Sectors, Comput. Phys. Commun. 269, 108124 (2021).
  179. H. Chen and Y. Jiang, A comprehensive framework for electroweak phase transitions: Thermal history and dynamics from bubble nucleation to percolation, arXiv:2503.00421.
  180. J. Kim, S. Lee, P. Sanyal, and J. Song, CDF W-boson mass and muon g-2 in a type-X two-Higgs-doublet model with a Higgs-phobic light pseudoscalar, Phys. Rev. D 106, 035002 (2022).
  181. S. J. Huber and M. Sopena, An efficient approach to electroweak bubble velocities, arXiv:1302.1044.
  182. Z. Kang, P. Ko, and T. Matsui, Strong first order EWPT & strong gravitational waves in Z3-symmetric singlet scalar extension, J. High Energy Phys. 02 (2018) 115.
  183. M. Chala, C. Krause, and G. Nardini, Signals of the electroweak phase transition at colliders and gravitational wave observatories, J. High Energy Phys. 07 (2018) 062.
  184. W. Y. Ai, B. Laurent, and J. van de Vis, Bounds on the bubble wall velocity, J. High Energy Phys. 02 (2025) 119.
  185. G. D. Moore and T. Prokopec, How fast can the wall move? A study of the electroweak phase transition dynamics, Phys. Rev. D 52, 7182 (1995).
  186. A. Megevand and A. D. Sanchez, Velocity of electroweak bubble walls, Nucl. Phys. B825, 151 (2010).
  187. W. Liu and Y. Wu, Testing leptogenesis from observable gravitational waves, arXiv:2504.07819.
  188. E. Adli et al., The compact linear e+e− collider (CLIC), arXiv:2503.24168.
  189. A. Djouadi, The anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rep. 459, 1 (2008).
  190. J. Bernon, J. F. Gunion, H. E. Haber, Y. Jiang, and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models: mh=125  GeV, Phys. Rev. D 92, 075004 (2015).
  191. J. Gu, H. Li, Z. Liu, S. Su, and W. Su, Learning from Higgs Physics at Future Higgs Factories, J. High Energy Phys. 12 (2017) 153.
  192. J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, madgraph5: Going beyond, J. High Energy Phys. 06 (2011) 128.
  193. A. Belyaev, N. D. Christensen, and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the standard model, Comput. Phys. Commun. 184, 1729 (2013).
  194. ATLAS Collaboration, Formulae for estimating significance, Report No. ATL-PHYS-PUB-2020-025.
  195. C. Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3, SciPost Phys. Codebases 2022, 8 (2022).
  196. J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens, and M. Selvaggi (DELPHES 3 Collaboration), DELPHES 3, A modular framework for fast simulation of a generic collider experiment, J. High Energy Phys. 02 (2014) 057.
  197. M. Boronat, J. Fuster, I. Garcia, E. Ros, and M. Vos, A robust jet reconstruction algorithm for high-energy lepton colliders, Phys. Lett. B 750, 95 (2015).
  198. M. Boronat, J. Fuster, I. Garcia, P. Roloff, R. Simoniello, and M. Vos, Jet reconstruction at high-energy electron–positron colliders, Eur. Phys. J. C 78, 144 (2018).
  199. M. Cacciari, G. P. Salam, and G. Soyez, FastJet user manual, Eur. Phys. J. C 72, 1896 (2012).
  200. G. L. Bayatian et al. (CMS Collaboration), CMS technical design report, volume II: Physics performance, J. Phys. G 34, 995 (2007).
  201. G. Bagliesi, Tau tagging at Atlas and CMS, in Proceedings of the 17th Symposium on Hadron Collider Physics 2006 (HCP 2006) (2007), arXiv:0707.0928.
  202. A. M. Sirunyan et al. (CMS Collaboration), Performance of reconstruction and identification of τ leptons decaying to hadrons and ντ in pp collisions at s=13  TeV, J. Instrum. 13, P10005 (2018).
  203. M. Proissl, Dijet invariant mass studies in the Higgs boson H→bb¯ resonance search in association with a W/Z boson using the ATLAS detector, Ph.D. thesis, Edinburgh University, 2014 [Report No. CERN-THESIS-2014-275].
  204. H. Abramowicz et al., Higgs physics at the CLIC electron–positron linear collider, Eur. Phys. J. C 77, 475 (2017).
  205. D. Kim, S. Lee, H. Jung, D. Kim, J. Kim, and J. Song, A panoramic study of K-factors for 111 processes at the 14 TeV LHC, J. Korean Phys. Soc. 84, 914 (2024).

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Phys. Rev. D 112, 055035– Published 24 September, 2025
  • Received 30 June 2025
  • Accepted 4 September 2025
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